Practitioner Seminar (for Students) and Frankfurt MathFinance Colloquium

• Der Förderverein Mathematik und das Institut für Mathematik veranstalten im Wintersemester 2024/25 die Ringvorlesung "Risiken auf Finanzmärkten und ihre Kontrolle". Link

• Berufspraxiskolloquium Finanzmathematik

  Alexander Molitor und Jochen Seitz (d-fine)
  Donnerstag, 4.7.2024, 18:15, Robert-Mayer Straße 10, Raum 110
  Titel: Ein Tag im Leben eines Quants bei d-fine: Bewertung ESG-gekoppelter Derivate

  Mit über 1000 Mitarbeiterinnen und Mitarbeitern ist d-fine eine der führenden Beratungsfirmen für technologisch-intensive und quantitative Projekte. In unserem Vortrag geben wir einen Einblick in die facettenreiche Arbeit unserer Quants. Wir skizzieren dabei einen typischen Arbeitstag, der von der mathematischen Modellierung komplexer Derivate über deren Implementierung bis zur Analyse der daraus resultierenden Bewertungsergebnisse reicht. Ein praktisches Beispiel, das die Bewertung von Derivaten umfasst, deren Auszahlungsprofil an Umwelt-, Sozial-, und Governance-Kriterien (ESG) gekoppelt ist, wird dabei anschaulich erklärt.
  
  Im Anschluss an den Vortrag lädt d-fine zu einem Get-together ein.

• Berufspraxiskolloquium Finanzmathematik

  DWS Group, Sebastian Kring (Fachvortrag), Roko Markesic (Firmenvorstellung)
  Donnerstag, 6.6.2024, 18:15, Robert-Mayer Straße 10, Raum 110
  Titel: Mehrperiodische Portfoliooptimierung mit Deep Reinforcement Learning

  Mehrperiodische Portfoliooptimierungsprobleme sind i.d.R. nicht einfach zu lösen. Für ausgewählte Problemstellungen existieren entweder analytische Lösungen oder man kann diese Optimierungsprobleme u. U. mittels numerischer Verfahren, wie z.B. dynamischer Programmierung, lösen. Deep Reinforcement Learning (DRL) eröffnet einen alternativen und flexiblen Ansatz, um optimierte Investmentstrategien für diese Fragestellungen abzuleiten. In dem Vortrag geht es darum, was DRL ist und wie es in der Praxis anhand von Fallbeispielen angewendet werden kann.

• Berufspraxiskolloquium Finanzmathematik

  Kristin Hasse, Niklas Könen, Janis Müller und Philipp Schröder (PricewaterhouseCoopers)
  Mittwoch, 15.5.2024, 18:15, Robert-Mayer Straße 10, Raum 110
  Titel: Valuation and Risk@PwC

  Der Vortrag vermittelt einen umfassenden Einblick in die Welt der Finanzinstrumente, deren Bewertung und Risikomodellierung. Im ersten Teil tauchen wir ein in die faszinierende Welt der Finanzmärkte und zeigen, wie Marktdaten und Bewertungsmodelle Entscheidungen beeinflussen. Mit einem Praxisbeispiel einer europäischen Swaption veranschaulichen wir, wie theoretische Konzepte in der realen Welt angewendet werden können. Im zweiten Teil befassen wir uns mit den wesentlichen Risiken, die sich aus Derivaten ergeben können, nämlich dem Marktrisiko, dem XVA-Risiko und dem Kontrahentenrisiko, und wie diese Risiken gemessen, kontrolliert und gesteuert werden können. Dabei behandeln wir Modellierungstechniken sowie externe Anforderungen und Marktstandards. Anhand einer europäischen Swaption zeigen wir dann konkret, wie das Marktrisiko modelliert und gemessen werden kann.

• Rhein-Main Kolloquium Stochastik

  David Prömel (University of Mannheim)
  Freitag, 7.7.2023, 15:15, Robert-Mayer Straße 10, Raum 711 groß
  Title: Model-free portfolio theory: a rough path approach

  Classical approaches to optimal portfolio selection problems are based on probabilistic models for the asset returns or prices. However, by now it is well observed that the performance of optimal portfolios are highly sensitive to model misspecifications. To account for various type of model risk, robust and model-free approaches have gained more and more importance in portfolio theory. Using rough path theory, we provide a pathwise foundation for stochastic Ito integration, which covers most commonly applied trading strategies and mathematical models of financial markets possibly under model uncertainty. Based on this pathwise foundation, we develop a model-free approach to stochastic portfolio theory and Cover's universal portfolio. The use of rough path theory allows for treating significantly more general portfolios in a model-free setting, compared to previous model-free approaches. The talk is based on joint works with Andrew Allan, Christa Cuchiero and Chong Liu.
  
  Christoph Czichowsky (London School of Economics), 16:45
  Title: Hedging and portfolio optimisation in rough volatility models

  
  Rough volatility models have become quite popular recently, as they capture both the fractional scaling of the time series of the historic volatility (Gatheral et al. 2018) and the behaviour of the implied volatility surface (Fukasawa 2011, Bayer et al. 2016) remarkably well. In contrast to classical stochastic volatility models, the volatility process is neither a Markov process nor a semimartingale. Therefore, these models fall outside the scope of standard stochastic analysis and provide new mathematical challenges. In this talk, we present an overview of of this new paradigm in volatility modelling and consider the impact of rough volatility on hedging and portfolio optimisation. The talk is based on joint works with David Martins, Johannes Muhle-Karbe and Denis Schelling.

• Berufspraxiskolloquium Finanzmathematik

  Kasra Khani, Alexander Molitor und Jochen Seitz (d-fine)
  Donnerstag, 17.11.2022, 18:15 im Raum 110
  Titel: Golden Copies, Modelle und Kalibrierung - Bewertung in der Praxis

  d-fine ist mit mehr als 1000 Mitarbeiter*innen eine der führenden deutschen Managementberatungen für quantitativ und technologisch anspruchsvolle Projekte. Nach einer Vorstellung des Unternehmens tauchen wir in den Projektalltag eines Mathematikers ein und veranschaulichen dabei anhand eines Swaps die praktischen Herausforderungen in der Bewertung von Finanzprodukten. In einem ersten Schritt stellen wir die benötigten theoretischen Modelle vor und gehen auf deren Kalibrierung ein. Abschließend widmen wir uns den zur Kalibrierung notwendigen Marktdaten und lernen den Begriff der Golden Copy kennen.
  
  Im Anschluss an den Vortrag lädt d-fine zu einem Get-together ein.

• Berufspraxiskolloquium Finanzmathematik

  Klaus Rinne (Ernst & Young, FAAS Quant Team)
  Donnerstag, 3.11.2022, 18:15 im Raum 711 groß
  Titel: Ermittlung des Kontrahentenausfallrisikos bei Derivaten

  Beim Abschluss von Derivaten besteht das Risiko, dass die Zahlungsverpflichtungen über die Laufzeit von der Gegenpartei nicht erfüllt werden können. Selbst wenn das Derivat bei Abschluss wertneutral ist, entsteht durch Marktbewertung des Underlying des Derivats im Laufe der Zeit ein Exposure. Im Rahmen des Vortrags werden verschiedene Ansätze zur Modellierung für einzelne Derivate und ganze Portfolien erläutert. Außerdem beleuchten wir die Risikominderungsstrategien und die Sichtweisen verschiedener Stakeholder innerhalb einer Bank.

• Berufspraxiskolloquium Finanzmathematik

  Patrick Liebrich (Emcore)
  Donnerstag, 23.6.2022, 18:15 im 711 groß
  Titel: Der Finanzplatz Liechtenstein

  Das Fürstentum Liechtenstein bietet durch seine Lage in der Schweizer Zollunion und dem EWR hervorragende steuerliche und rechtliche Rahmenbedingungen. So ist der Kleinstaat Sitz vieler europäisch agierender Finanzdienstleister. Und doch unterscheidet sich die Art der hier ansässigen Unternehmen deutlich von denen in den grossen Finanzzentren wie Frankfurt. In dem Vortrag wird der Finanzplatz Liechtenstein mit seinen Besonderheiten vorgestellt.

• Berufspraxiskolloquium Finanzmathematik

  Christian Braun und Nadine Mbenda (PricewaterhouseCoopers | Risk & Regulation)
  Donnerstag, 9.12.2021, 18:15 per Zoom
  Titel: Quantitatives Kreditrisikomanagement: Einführung und aktuelle Herausforderungen

  Das Credit Risk Quant-Team von PwC Deutschland wird die Dimensionen des Kreditrisikos, wesentliche Risikomodelle, die Ermittlung der Risikovorsorge unter IFRS 9 und die aktuellen Herausforderungen bei der Kreditrisikomodellierung vorstellen.

• Berufspraxiskolloquium Finanzmathematik

  Klaus Rinne (Ernst & Young, FAAS Quant Team)
  Donnerstag, 28.10.2021, 16:15 per Zoom
  Titel: Valuation of interest rate options under negative rates

  Table of Content: - Introduction to the concept of volatility - Interest rate cap & floor - Working as a quant at EY
  
  Zugangsdaten werden den Studierenden im Bachelor/Masterstudiengang Mathematik zugeschickt. Alternativ können sie bei Frau Prinz-de Kluidt angefragt werden.

• Berufspraxiskolloquium Finanzmathematik

  Kasra Khani, Hans-Peter Wächter (d-fine)
  Dienstag, 29.6.2021, 14:15 per Zoom
  Titel: The Endgame of Libor ? Einstieg als Finanzmathematiker in einer Zeit voller Veränderungen

  d-fine ist mit mehr als 1000 Mitarbeiterinnen und Mitarbeitern eines der führenden Beratungsunternehmen für quantitativ und technologisch anspruchsvolle Projekte. Nach einer Vorstellung der Firma möchten wir Ihnen gerne die Benchmark Reform im Rahmen von USA Studentenkrediten vorstellen. Unser Vortrag thematisiert hierbei insbesondere den Projektalltag und die besonderen Erfahrungen als Einsteiger in Zeiten der Pandemie.

• Berufspraxiskolloquium Finanzmathematik

  Jürgen Bierbaum (Alte Leipziger Lebensversicherung)
  Donnerstag, 5.12.2019, 16:15, Raum 711 groß
  Titel: Bewertung in unvollständigen Märkten - Finanzmathematik in der Lebensversicherung

  Die Mehrzahl der Lebensversicherungsverträge in Deutschland enthält langfristige Zinsgarantien. Die Preisfindung sowie die ökonomische und bilanzielle Bewertung dieser Verträge erfordert die Entwicklung komplexer finanz- und versicherungsmathematischer Modelle. Wegen der Illiquidität der Märkte für langfristige Kapitalanlagen ist auch die Kalibrierung der Bewertungsmodelle eine nichttriviale Aufgabe. Zusätzlich sollte bereits beim Produktdesign auf eine kapitaleffiziente Struktur der Verpflichtungen geachtet werden. Im Vortrag werden einige wichtige Aufgabenstellungen aus der Praxis sowie gängige Ansätze zu ihrer Lösung vorgestellt.

• MathFinance Colloquium

  Jiling Cao (Auckland University of Technology)
  Monday, 2.9.2019, 17:15, Raum 711
  Titel: Inferring information from the S&P 500 and CBOE indices: The more the merrier ?

  The Chicago Board Options Exchange (CBOE) updated the CBOE Volatility Index (VIX) in 2003 and further launched the CBOE Skew Index (SKEW) in 2011, in order to measure the 30-day risk-neutral volatility and skewness of the S&P 500 Index (SPX). In this work, we mainly compares the information extracted from the SPX and CBOE indices in terms of the SPX option pricing performance. Based on our analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while, the SKEW is very noisy and does not contain much important information for option prices.

• Berufspraxiskolloquium Finanzmathematik

  Sebastian Becker, Nor Jaafari (Zenai AG)
  Donnerstag, 25.4.2019, 16:15, Raum 110
  Titel: Machine Learning und Artificial Intelligence bei Zenai

  Zenai ist ein auf financial machine learning spezialisiertes Startup mit Sitz in Zürich (Schweiz). Seit der Gründung im Jahr 2017 konzentrieren wir uns auf die Entwicklung von ML-Lösungen, die einerseits auf Modellen basieren, andererseits aber auch rein von Daten getrieben sein können. Zusätzlich beraten wir unsere Kunden auch hinsichtlich der Themen machine learning und artificial intelligence. In unserem Vortrag stellen wir den Arbeitsalltag eines Mathematikers bei Zenai anhand von ausgewählten Beispielen vor. Zusätzlich geben wir einen kurzen Einblick in das Pricing/Hedging von hochdimensionalen amerikanischen Optionen mittels neuronaler Netze und stellen das Konzept des goal based investing mittels probablistic scenario optimization vor.

• Berufspraxiskolloquium Finanzmathematik

  Nikolai Dördrechter, Lukas Elbert, Marcel Zeuch (XTP)
  Donnerstag, 15.11.2018, 16:15, Raum 110
  Titel: XTP-Vortrag im Berufspraxiskolloquium Finanzmathematik

  XTP ist Markführer in der Implementierungseffizienz im institutionellen Asset Management. Unsere Kunden sind große institutionelle Investoren wie Pensionskassen, Versicherer und Rückversicherer. Mit Hilfe unserer datengetriebenen, forensischen Analysen schaffen wir Transparenz über Kosten, Risiken und Performance im Kapitalanlageprozess aller Assetklassen. Grundlage unserer Tätigkeit ist ein profundes Verständnis der globalen Kapitalmärkte. Wir haben einen holistischen Blick auf den Kapitalanlageprozess vom Asset Management, Handel, Fondsadministration bis hin zur Verwahrstelle. Mit unseren proprietären Software-Tools und in-house Benchmarking-Datenbanken haben wir bereits mehr als EUR 2,5 Billionen an Assets analysiert. Unsere Kunden profitieren von einer risikolosen Zusatzrendite. Unsere Arbeit hat einen guten Zweck ? die durch uns erzielten Einsparungen führen ultimativ zu höheren Renten. So reduzieren wir die Informationsasymmetrie und tragen dazu bei, die Fairness, Transparenz und Effizienz des Finanzsektors zu erhöhen. Die Analyse von expliziten und impliziten Transaktionskosten ist ein zentraler Bestandteil unserer quantitativen Arbeit. Wir stellen als Beispiel eine empirische Analyse zu Transaktionskosten im Bond Bereich vor, präsentieren ein Pre-Trade Market Impact Modell für Aktientransaktionen und geben erste Einblicke in ein Modell zur Berechnung von Asset Management-Performance Fees, das Monte-Carlo Simulationen nutzt.

• Berufspraxiskolloquium Finanzmathematik

  Björn Ulbricht (DZ Bank)
  Donnerstag, 25.10.2018, 16:15, Raum 110
  Titel: Risikocontroller in der DZ Bank

  Die DZ BANK AG gehört mehrheitlich den mehr als 900 Genossenschaftsbanken in Deutschland. Als Zentralbank und Spitzeninstitut hat sie den Auftrag, die Geschäfte der vielen eigenständigen Genossenschaftsbanken vor Ort zu unterstützen und ihre Position im Wettbewerb zu stärken. Wie funktioniert das genossenschaftliche Finanzgruppenprinzip? Welche Rolle spielt dabei die DZ Bank? Ein Eckpfeiler beim genossensschaftlichen Finanzgruppenprinzip ist ein gutes Risikomanagement der DZ Bank, bei der das Risiko der Genossenschaftsbanken allokiert wird. Um etwas über Risiken von Geschäfften sagen zu können, ist es nötig die Risiken zu quantifizieren. Hierbei spielen vor allem mathematische Modelle eine Rolle, welche an Marktdaten kalibriert werden und unter gewissen Verteilungsannahmen etwas über die Risiken der zukünftigen Wertentwicklung der Geschäfte sagen soll. Die daraus resultierenden Kenngrößen (z.B. VaR) werden sowohl für die interne Steuerung als auch für die Ermittlung des regulatorisch zu hinterlegeneden Eigenkapitals genutzt. Ein derzeit aktuelles Thema in der Bankenwelt ist die Änderung des Marktstandards für Swaptions im Euro-Raum. Die liquidisten Produkte sind sogenannte Cash-Settled Swaptions. Diese wurden bisher stets unter vereinfachten Annahmen mit einer nicht-arbitragefreien Formel gepreist. Diese Annahme beeinflusst vor allem die Bewertung von "deep In-The-Money" Swaptions. Durch das aktuelle Niedrigzinsumfeld, werden die Swaption Bücher der Marktteilnehmern durch ITM Receiver Swaptions dominiert. Aufgrund der Modellunsicherheit wurden diese sehr illiquide und deren Bid-Ask Spreads haben zum Teil ihren Zeitwert überschritten. Daher wird ab Oktober 2018 eine neue Bewertungsformel als Marktstandard und der standardmäßige Abschluss von "Physical Settled Swaptions" im EUR Interbankenraum eingeführt.

• Berufspraxiskolloquium Finanzmathematik

  Roland Seydel (Commerzbank)
  Mittwoch, 15.11.2017, 16:15, Raum 711 groß
  Titel:Model Validation at Commerzbank

  After a short general introduction to Commerzbank and its model validation framework, we will focus on several (validation) case studies where knowhow in (financial) mathematics is more and less useful. (The language of the talk will depend on the wishes of the audience.)

• MathFinance Colloquium

  Giorgio Ferrari (University of Bielefeld)
  Thursday, October, 26, 2017, 6.15 pm
  Math building, Robert-Mayer Straße 6-10, 7th floor, Raum 711 groß
  Title: On the Optimal Management of Public Debt: a Singular Stochastic Control Problem

  Consider the problem of a government that wants to reduce the debt-to-GDP (gross domestic product) ratio of a country. The government aims at choosing a debt reduction policy which minimises the total expected cost of having debt, plus the total expected cost of interventions on the debt ratio. We model this problem as a singular stochastic control problem over an infinite time-horizon. In a general not necessarily Markovian framework, we first show by probabilistic arguments that the optimal debt reduction policy can be expressed in terms of the optimal stopping rule of an auxiliary optimal stopping problem. We then exploit such link to characterise the optimal control in a two-dimensional Markovian setting in which the state variables are the level of the debt-to-GDP ratio and the current inflation rate of the country. The latter follows uncontrolled Ornstein-Uhlenbeck dynamics and affects the growth rate of the debt ratio. We show that it is optimal for the government to adopt a policy that keeps the debt-to-GDP ratio under an inflation-dependent ceiling. This curve is given in terms of the solution of a nonlinear integral equation arising in the study of a fully two-dimensional optimal stopping problem.

• Berufspraxiskolloquium Finanzmathematik

  Matthias Riedel (d-fine)
  Mittwoch, 28.6.2017, 16:15, Raum 110
  Titel:Als Mathematiker (m/w) im Bereich Risiko und Finanzen -- Vorstellung d-fine

  d-fine ist mit mehr als 600 Beratern einer der führenden Anbieter für quantitative und technisch anspruchsvolle Projekte. Nach einer Vorstellung der Firma wird durch Projektbeispiele ein Einblick in die Projektarbeit und die dabei relevanten Fragestellungen und Herangehensweisen präsentiert.
  
  Im Anschluss an den Vortrag lädt d-fine zu einem Come-together ein.

• Berufspraxiskolloquium Finanzmathematik

  Gerrit Handrich (Deutsche Finanzagentur)
  Mittwoch, 3.5.2017, 16:15, Raum 110
  Titel: Steuerung des Schuldenportfolios der Bundesrepublik

  Für den Bund als den Benchmark-Emittenten im Euroraum stellt die Finanzagentur eine möglichst kostengünstige und risikoarme Finanzierung sicher. Die Grundlage für die Portfoliosteuerung bilden Zinsmodelle und Optimierungstechniken. Die Darstellung der vereinfachten Grundlagen eröffnet den Blick auf die Rolle, welche diese in der komplexen Entscheidungsfindung spielen.

• Berufspraxiskolloquium Finanzmathematik

  Maximilian Stroh (Quoniam Asset Management)
  Mittwoch, 25.1.2017, 16:15, Raum H1 im 1. Stock des Jügelhauses (Hörsaalgebäude Bockenheim)
  Titel: Quantitative Investment Engineering -- Als Mathematiker bei Quoniam

  Quoniam Asset Management ist eine zur Union Investment Gruppe gehörende Investmentboutique, die seit fast 17 Jahren auf das aktive Management von Aktien-, Renten- und Multi-Asset-Mandaten spezialisiert ist. Quoniam betreut für mehr als 120 Kunden Assets in Höhe von mehr als 26 Milliarden Euro. Nach einer kurzen Firmenvorstellung werden verschiedene berufliche Möglichkeiten von Mathematikern im Asset Management vorgestellt. Abschließend werden typische Fragestellungen im Quant Research anhand von zwei einfachen Beispielen illustriert.

• Rhein-Main Kolloquium Stochastik

  Christian Bender (Universität des Saarlandes)
  Freitag, 15.7.2016, 15:15, Robert-Mayer Straße 10, Raum 711 groß
  Title: A first order backward stochastic partial differential equation for swing option pricing

  We study an optimal control problem related to swing option pricing in a general non- Markovian setting in continuous time. As a main result we uniquely characterize the value process in terms of a first-order non-linear backward stochastic partial differential equation (BSPDE). Under mild assumptions, the value process of the optimal control problem turns out to be continuously differentiable in the space variable (that represents the volume which the holder of the option can still exercise up to maturity). This observation gives rise to an existence and uniqueness result for the corresponding BSPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales. The talk is based on joint work with Nikolai Dokuchaev (Curtin University, Perth).
  
  Frank Riedel (Universität Bielefeld), 16:45
  Title: Financial Equilibria under Knightian Uncertainty about Volatility

  
  In diffusion models, few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow-Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow-Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow-Debreu equilibrium allocations are generically unattainable by dynamically trading few long-lived assets.

• Berufspraxiskolloquium Finanzmathematik

  Christian Böinghoff (Deutsche Bundesbank)
  Mittwoch, 6.7.2016, 16:15, Robert-Mayer Straße 10, Raum 110
  Titel: Modelleprüfer bei der Deutschen Bundesbank - Hessen, Deutschland und Europa

  In dem Vortrag werden die Tätigkeit eines quantitativen Bankenprüfers bei der Deutschen Bundesbank sowie der Arbeitgeber Deutsche Bundesbank vorgestellt. Neben einer kurzen Einführung in die Aufgaben und Herausforderungen im Rahmen der einheitlichen europäischen Bankenaufsicht (SSM), wird am Beispiel eines einfachen Kreditportfoliomodells auch auf Risikomodellierung in Banken eingegangen.

• Mathematisches Kolloquium

  Christoph Czichowsky (London School of Economics)
  Freitag, 10.6.2016, 16:15, Robert-Mayer Straße 10, Raum 711 groß
  Title: Portfolio Optimisation, Transaction Costs, Shadow Prices and Fractional Brownian Motion

  In financial mathematics, one classically works with so-called frictionless markets, where arbitrary amounts of stocks can be bought and sold at each time for the same price. Under this assumption, the absence of arbitrage opportunities (riskless profits) implies that price processes have to be semimartingales, that is, stochastic processes which are ``good'' integrators. While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingale models based on fractional Brownian motion can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. Such models have been proposed by Benoit Mandelbrot more than fifty years ago because of their natural fractional scaling and related statistical properties. In this talk, I will present an overview over several results that provide a way how to use non-semimartingale price processes such as the fractional Black-Scholes model in portfolio optimisation under proportional transaction costs by establishing the existence of a so-called shadow price. This is a semimartingale price process, taking values in the bid ask spread, such that frictionless trading for that price process leads to the same optimal strategy and utility as the original problem under transaction costs. The talk is based on joint work with Walter Schachermayer.

• Ulrike Zymolka
  Thursday, April, 21, 2016, 6.15 pm, Robert-Mayer Straße 6-8, Raum 302 (Hilbertraum)
  Titel: A practical approach for constructing an arbitrage-free volatility surface

  Generating an arbitrage-free volatility surface is essential for pricing and risk management of volatility dependent financial products like swaptions or CMS, among others. In practice, the challenge is quite often to balance computing times and accuracy in the construction process of volatility surfaces. In the absence of closed form solutions, approximation formulas like the well-known one from Hagan for swaptions are used. This proxy in particular has often an essential flaw - violating the no-arbitrage condition. The talk presents a practical approach to overcome this problem, also showing further benefits for the calibration to the market.

• Berufspraxiskolloquium Finanzmathematik

  Sadik Iliman (KPMG)
  Mittwoch, 20.4.2016, 16:15, 711 groß
  Titel: Kreditrisikoangepasste Bewertung von OTC Derivaten

  Zusammenfassung: Ausgehend vom fundamentalen Prinzip der risikoneutralen Bewertung von Derivaten werden Methoden präsentiert, um Kontrahentenausfallrisiken in Derivategeschäften in die risikoneutrale Bewertung einzupreisen. Die vorgestellten Methoden basieren auf dem derzeitigen Marktstandard und werden auf Basis von Beispielen demonstriert. Abschließend wird ein kurzer Ausblick in weitere aktuelle Themen bzgl. der Adjustierung der risikoneutralen Bewertungsformel vorgestellt.
  
  Zu Beginn des Vortrags wird die KPMG kurz vorgestellt und im Anschluss lädt die KPMG alle Teilnehmer zu einem Get-together ein.

• Berufspraxiskolloquium Finanzmathematik

  Adrian Zymolka (Axioma Deutschland), Mittwoch, 20.1.2016, 16:15
  Math building, Robert-Mayer Straße 6-8, Raum 302 (Hilbertraum)
  Titel: Robuste Portfolio-Optimierung mit Axioma

  Axioma ist ein führender Anbieter von quantitativen Werkzeugen für das Portfolio-Management. Neben einer modernen Risk-Management-Plattform, Multi-Faktor-Risikomodellen und Performancemessung bieten wir auch flexible und innovative Portfolio-Optimierung an. Eines der neueren Konzepte in der Finanzpraxis ist Robuste Optimierung, die Schätzfehler zu wichtigen Parametern explizit in den Optimierungsprozess einbeziehen kann. Dadurch wird die Portfoliokonstruktion weitgehend immun gegen kleine Schwankungen der wesentlichen Inputgrößen und führt zudem im Zeitverlauf oft zu weniger Turnover. Basierend auf der Markowitz-Theorie werden die praktischen Aspekte der Methodik vorgestellt und die Vorteile anhand experimenteller Resultate belegt.

• Klebert Kentia Tonleu (HU Berlin), Wednesday, September, 16, 2015, 3.15 pm
  Math building, Robert-Mayer Straße 10, 7th floor, Raum 711 klein
  Title: Topics on First- and Second-Order Backward SDEs with Applications

  In this talk, we present some results on the theories of first- and second-order backward stochastic differential equations (BSDEs), with applications oriented towards no-good-deal valuation in mathematical finance. The first part of the talk focuses on new wellposedness and comparison results for BSDEs driven by random measures of jumps that are possibly of infinite activity, with BSDE generators not necessarily Lipschitz in the jump-integrand. In the second part, we provide an overview of second-order BSDEs with Lipschitz generators, which are useful in studying stochastic control problems posed in terms of mutually singular probability measures. As application, we consider no-good-deal valuation in financial markets with volatility uncertainty. The talk is based on joint works with D. Becherer and M. Büttner.

• Pierre Garreau, Thursday, February, 5, 2015, 6.15 pm
  Math building, Robert-Mayer Straße 6-10, 3rd floor, Raum 302 (Hilbertraum)
  Title: A Structural Jump Threshold Framework for Credit Risk

  We present a new structural framework for multidimensional default risk. We define the time of default as the first time the log-return of the stock price of a firm jumps below a (possibly nonconstant) default level. When stock prices are exponential Levy, this framework is equivalent to a reduced form approach, where the intensity process is parametrized by a Levy measure. The dependence between the default times of firms within a basket of credit securities is the result of the jump dependence of their respective stock prices, making the link between the equity and credit markets. We value a first-to-default basket CDS as an application. Joint work with Alec Kercheval.

• Oliver Kley (TU Munich), Thursday, November, 27, 2014, 4.30 pm
  Math building, Robert-Mayer Straße 6-10, 3rd floor, Raum 302 (Hilbertraum)
  Title: Systemic risk in a large claims insurance market with bipartite graph structure

  We model business relationships exemplified for an insurance market by a bipartite graph which determines the sharing of severe losses. Using Pareto-tailed losses and multivariate regular variation we obtain asymptotic results for systemic risk measures which are based on the Value-at-Risk and the Expected Shortfall. We show that the dependence on the network structure plays a fundamental role in their asymptotic behaviour. As is well-known, if the Pareto exponent is larger than 1, then for the individual agent (re-insurance companies) diversication is beneficial, whereas when it is less than one, concentration on a few objects is the better strategy for individual agents. The situation, however, changes, when systemic risk comes into play. The random network structure has a strong influence on diversification effects, which destroys this simple single agent's diversification rule. It turns out that diversification is always beneficial from a macroscopic point of view creating a conflicting situation between the incentives of single agents and the interest of some superior entity to keep overall risk small. We explain the influence of the network structure on diversification effects in different network scenarios.
  
  5.40 pm Coffee break
  
  Tom Fischer (Würzburg University), Thursday, November, 27, 2014, 6.00 pm
  Math building, Robert-Mayer Straße 6-10, 3rd floor, Raum 302 (Hilbertraum)
  Title: Valuation in the structural model of systemic interconnectedness

  
  This presentation summarizes some previously published and several to-date unpublished results for an asset and derivatives pricing model which accounts for systemic counterparty risk in a structural manner. The model allows for the cross-ownership of equities and liabilities within a network of financial entities. Assets and liabilities within the system, as well as the corresponding ownership structures, are allowed to depend on the prices of system-exogenous assets. Liabilities, which can also be derivatives of system-exogenous or system-endogenous assets, belong to one of potentially many seniority classes, whose order of priority is properly incorporated. The presented work generalizes some of the results by Eisenberg and Noe, Suzuki, Elsinger, and Gourieroux et al., and can be understood as a far-reaching extension of the Merton model. Of particular concern are the existence and the uniqueness of price solutions, as well as the existence of greatest (i.e. globally Pareto-dominant) solutions when multiple equilibria exist. In the latter case, unambiguous risk-neutral pricing of all liabilities might still be possible. In line with previous results by Elsinger, the value of a system outsider's holdings is always uniquely determined, and -- for the group of all system outsiders and bankruptcy costs absent -- it never pays to bail out defaulting entities.

Talks Sommer Term 2014 

• Thilo Meyer-Brandis (LMU Munich), Thursday, July, 17, 2014, 6.15 pm
  Math building, Robert-Mayer Straße 10, Raum 711 groß
  Title: Risk-Consistent Conditional Systemic Risk Measures

  In this paper we provide an axiomatic approach to the class of risk-consistent conditional systemic risk measures. This class consists of multivariate conditional risk measures which can be decomposed into a conditional aggregation function and a conditional univariate risk measure. The axiomatic characterization for this class of decomposable systemic risk measures was introduced by Chen et. al. (2013) for a finite probability space and in an unconditional framework. We extent this characterization in different ways. We allow for a more general probability space and extend the framework to a conditional setting. Furthermore we reduce/generalize the required properties of systemic risk measures in order to allow for a more flexible structure. We will conclude by looking at some concrete systemic risk measures in a simulation study.

Talks Winter Term 2013/14 

• Budhi Arta Surya (SBM ITB), Thursday, October, 31, 2013, 6.15 pm
  House of Finance, Deutsche Bank Lecture Room
  Title: Optimal Capital Structure with Scale Effects under Spectrally Negative Levy Models

  The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of bankruptcy costs and tax benefits dependent on the firm's asset value. These effects have been empirically shown, among others, in Warner (1976), Ang et al. (1982), and Graham and Smith (1999). By using the fluctuation identities for the spectrally negative Levy process, we obtain a candidate bankruptcy level as well as a sufficient condition for optimality. The optimality holds in particular when, monotonically in the asset value, the value of tax benefits is increasing, the loss amount at bankruptcy is increasing, and its proportion relative to the asset value is decreasing. The solution admits a semi-explicit form, and this allows for instant computation of the optimal bankruptcy levels, equity/debt/firm values and optimal leverage ratios. A series of numerical studies are given to analyze the impacts of scale effects on the default strategy and the optimal capital structure. Joint work with Kazutoshi Yamazak

Talks Summer Term 2012 

• Roland Seydel (Deutsche Finanzagentur), Thursday, May, 24, 2012, 5.15 pm
  Math building, Robert-Mayer Straße 10, Raum 711 groß
  Title: Grill dir einen Wurm -- Optimale Würfelstrategien und Optionsbewertung

  Im Würfelspiel "Heckmeck am Bratwurmeck" (Reiner Knizia, Zoch-Verlag, 2005) ist es das Ziel, durch wiederholtes Würfeln ein möglichst hohes Würfelergebnis zu erzielen --- aber Vorsicht, am Ende des Würfelns muss auf jeden Fall mindestens ein Wurm gewürfelt worden sein, sonst war alles umsonst. Möchte man eine optimale Würfelstrategie errechnen, fallen Parallelen zur Bewertung von Optionen an den Finanzmärkten auf: Etwa gibt es Early Exercise (wenn man aufhört zu würfeln), es gibt Knock Out (etwa wenn kein Wurm gewürfelt wurde), und man möchte einen möglichst hohen "Preis" erzielen. In meinem Vortrag möchte ich auf diese Parallelen eingehen, und dabei spielerisch einige wichtige Prinzipien der Optionsbewertung einführen. Wir lösen das Problem mathematisch und numerisch am Computer, unter Zuhilfenahme der in der Steuerungstheorie üblichen sogenannten Wertfunktion, die letztlich den Wert der "Würfel-Option" angibt. In der Praxis stellt sich jedoch heraus, dass auch eine theoretisch optimale Würfelstrategie nicht den Gewinn garantiert --- es kommt wie an der Börse immer auf die Mitspieler an!

Talks Winter Term 2011/12 

• Johannes Muhle-Karbe (ETH Zürich), Thursday, February, 16, 2012, 5.15 pm
  House of Finance, Deutsche Bank Lecture Room
  Title: Transaction Costs, Trading Volume, and the Liquidity Premium

  In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly. (Joint work with Stefan Gerhold, Paolo Guasoni, and Walter Schachermayer).

• Claas Becker (Deutsche Bank), Thursday, October, 20, 2011, 5.15 pm
  Math building, Robert-Mayer Straße 10, Room 110 (first floor)
  Title: A mathematical introduction to securitization

  Securitization has been identified as one of the ingredients of the current financial crisis. We give an introduction to securitization and discuss the different mathematical models used for rating securitization tranches and for trading.

Talks Summer Term 2011 

• Jaksa Cvitanic (California Institute of Technology), Friday, July, 29, 2011, 2:30 pm
  House of Finance, Deutsche Bank Lecture Room
  Title: Complete Market Equilibrium with Heterogeneous Agents

  In this talk we survey recent results on equilibrium models in a complete, continuous time financial market when investors have three possible sources of heterogeneity. Investors may differ in their beliefs, in their level of risk aversion and in their time preference rate. We study the impact of investors heterogeneity on the market price of risk, the stock price and volatility, as well as on the optimal portfolio strategies. We show that under natural cyclicality conditions, the market price of risk is countercyclical and the stock price exhibits excess volatility. We relate the heterogeneous economy with the family of associated homogeneous economies with only one class of investors, and we study asymptotic survival of various agents in the economy

Talks Winter Term 2010/11 

• Bodo Huckestein (d-fine), Thursday, February, 17, 2011, 5.15 pm
  House of Finance, Deutsche Bank Lecture Room
  Title: Risk modelling for private equity

  Equity investments are risky. There are two major components to the risk of an equity investment: the risk that the investment is lost in a default of the investment target; and the risk that the investor can only exit the investment with a loss. For publicly traded equity, these risks are known as counterparty risk and market risk. The transparency of the market provides a large amount of information and a wide range of methods is available to model these risks. In contrast, information is scarce for private equity investments limiting the usefulness of elaborate models. The task at hand is then to design a model of private equity risk that is as simple as possible while still capturing the essential features of the problem. We will present such a model and show that it is capable of providing expected loss and economic capital figures suitable for risk management.

• Rüdiger Frey (University of Leipzig), Thursday, January, 27, 2011, 5.15 pm
  House of Finance, Deutsche Bank Lecture Room
  Title: Nonlinear Black Scholes Equations in Finance: associated Control Problems and properties of Solutions

  We study properties of solutions to fully nonlinear versions of the standard Black-Scholes partial differential equation. These equations have been introduced in financial mathematics in order to deal with illiquid markets or with stochastic volatility. We show that typical nonlinear Black-Scholes equations can be viewed as dynamic programming equation of an associated control problem. We establish existence and comparison results and show that the equation induces a convex risk measure on the set of all continuous terminal value claims. Moreover, we study the asymptotic behavior of solutions as market frictions get `large'. Finally the pricing of individual contracts relative to a book of derivatives is discussed.

• Am 26. November 2010 um 16:00 Uhr findet im Festsaal der Universität (Campus Westend) die 17. Gauß Vorlesung statt.
  Veranstalter ist die DMV und der Fachbereich Informatik und Mathematik der Goethe-Universität. Den Hauptvortrag hält
  Walter Schachermayer (Uni Wien)
  Titel: Die Dualität des Geldes
  Nähere Informationen zu der Veranstaltung gibt es hier

Talks Summer Term 2010 

• Ulrich Horst (HU Berlin), Thursday, July, 1, 2010, 5.15 pm
  House of Finance, Room Dubai (first floor)
  Title: Equilibrium Pricing in Incomplete Markets under Translation Invariant Preferences

  We consider a partial equilibrium framework within which to price financial securities in dynamically incomplete markets in discrete time when the agents have translation invariant preference functionals. We show that the existence of equilibrium is equivalent to the existence of a representative agent which, in turns, is satisfied if the agents are sensitive to large losses. It turns out that the analysis of equilibrium in dynamic models can be reduced to a recursive sequence of static equilibrium models and when the flow of information is generated by independent random walks the equilibrium dynamics can be described by a coupled system of backward stochastic difference equations. This renders our theoretical analysis readily amenable to numerical simulations. We use numerical simulations to explain the frequently observed "volatility smiles" in terms of investor charaterstics. This talk is based on joint work with Patrick Cheridito, Michael Kupper and Traian Pirvu

• Sergey N. Smirnov (State University Higher School of Economics Moscow and FERM Lab), Friday, June, 18, 2010, 10.00 am
  Math building, Robert-Mayer Straße 10, Room 711 groß
  
  Prof. Smirnov will give a talk on some problems of financial engineering. Namely
  
  -Applications of portfolio credit risk analysis for determining deposit insurance fund adequacy
  
  -Stochastic modelling of term structure of interest rates, realistic with no arbitrage
  
  -Data filtering and recovery of missing data, achieving correct estimates of correlations
  
  -Margining portfolios of futures and options on futures, an approach for a low liquidity market

• Jeannette Woerner (TU Dortmund), Thursday, June, 10, 2010, 5.15 pm
  House of Finance, Room Dubai (first floor)
  Title: Detecting and capturing correlation in financial data

  Recently there have been proposed different methods for analyzing the empirical characteristics of financial data, e.g. behaviour of realized volatility, a certain correlation structure and paths regularity. Possible models capturing these features are models based on fractional Brownian motion. Another possibility is to consider fractional L\'{e}vy processes instead which combine the desirable properties of L\'{e}vy processes with the correlation structure of fractional Brownian motion. We consider different types of data, such as tick-by-tick stock data, daily index data and electricity data and show that their specific characteristic features, such as semiheavy tails, short- or long-range dependence and spikes may be reproduced by this class of processes.

• Hong Liu (Washington University in St.Louis OLIN Business School), Wednesday, June 9, 2010, 5.15 pm
  House of Finance, Deutsche Bank lecture hall
  Title: Asymmetric Information, Endogenous Illiquidity, and Asset Pricing With Imperfect Competition

  We use a novel framework that integrates standard asset pricing and microstructure models to study how asymmetric information, imperfect competition among market makers, and risk aversion affect equilibrium illiquidity and asset pricing. All the main results are obtained in closed-form. In our model, market power, asymmetric information, and market-making cost drive market illiquidity. This model can potentially explain some of the puzzling empirical findings such as (1) the bid-ask spread can be lower with asymmetric information; (2) the bid-ask spread can be positively correlated with trading volume; (3) stock volatility tends to decrease trading volume; (4) the bid-ask spread is positively correlated with market makers' inventory; (5) trading volume may increase with information asymmetry. In addition, we find that information asymmetry may reduce the welfare loss due to market power. Furthermore, the equilibrium number of market makers decreases with the market-making cost and increases with trading volume, and may increase with information asymmetry.

• Johannes Muhle-Karbe (University of Vienna), Thursday, May, 20, 2010, 5.15 pm
  House of Finance, DZ Bank lecture hall
  Title: Asymptotics and Exact Pricing of Options on Variance

  We consider the pricing of options written on the discrete realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the short term limits of call options on both objects. We find that the difference strongly depends on whether or not the stock price process has jumps. To study the exact valuation of options on the discrete realized variance itself, we then propose a novel randomization approach that allows to apply Fourier-Laplace techniques to price European-style options efficiently. To illustrate our results, we also present some numerical examples (joint work with Martin Keller-Ressel, ETH Zurich)

• Jerome Detemple (Boston University), Tuesday, May 11, 2010, 5.15 pm, House of Finance, DZ Bank lecture hall
  Title: Optimal Portfolio Allocations with Hedge Funds

  This paper analyzes optimal investment decisions, in the presence of non-redundant hedge funds, for investors with constant relative risk aversion. Factor regression models with option-like risk factors and no-arbitrage principles are used to identify and estimate the market price of hedge fund risk, the volatility coefficients of hedge fund returns and the correlation between hedge fund and market returns. Timing ability causes stochastic fluctuations in these return characteristics. Outside investors optimally hold hedge funds for diversification purposes and are motivated to hedge fluctuations in return components caused by timing ability. The paper examines the portfolio structure and behavior and the impact of timing and selection abilities. Incorporating carefully selected hedge fund classes in asset allocation strategies can be a source of economic gains.

• Alexander Schied (Mannheim University), Thursday, April, 15, 2010, 5.15 pm
  House of Finance, Commerzbank lecture hall (E.22)
  Title: Mathematical aspects of market impact modeling

  A market impact model describes the feedback of trading strategies on the underlying asset price. In the first part of this talk we will discuss various mathematical aspects of market impact models with transient price impact. We are in particular interest in the viability of a market impact model and discuss viability issues. In the next part, we will discuss further qualitative issues of maket impact.

Previous Talks  

• Vortrag zum Jahr der Mathematik

  Hans Föllmer (HU Berlin), Montag, 16 Juni 2008, 17:00 Aula der Universität, Campus Bockenheim
  Title: Finanzielles Risiko: Was kann die Mathematik dazu sagen?
  
  Anschließend an den Vortrag Empfang im Foyer
  
  

• Hans-Peter Deutsch (d-fine), Wednesday, April 30, 2008, 14:15 Room 711 groß (seventh floor), Robert-Mayer-Str. 10, Faculty of Mathematics, wissenschaftlicher Vortrag und Firmenvorstellung
  
  Title: Martingale und der Marktpreis des Risikos

  Es wird gezeigt, dass Arbitragefreiheit (also die Unmoeglichkeit, ohne Kapitaleinsatz und ohne Risikouebernahme sicheren Gewinn zu erwirtschaften) aequivalent ist zu der Existenz einen Wahrscheinlichkeitsmasses, bzgl. dessen die (geeignet normierten) Preise aller handelbaren Finanzinstrumente Martingale sind. Der Uebergang zwischen dem Wahrscheinlichkeitsmass der realen Welt und diesem Martingalmass geschieht gemaess des Girsanov-Theorems durch ein Drift-Transformation. Diese Drift-Transformation ist gegeben durch den Marktpreis des Risikos. Diese Erkenntnisse lassen sich zur Bewertung aller Finanzinstrumente benutzen. Es zeigt sich, dass der heutige Wert eines Finanzinstruments gleich seinem abdiskontierten zukuenftigen Erwartungswert ist, wobei dieser Erwartungswert bzgl. des Martingalmasses (und NICHT bzgl. der Wahrscheinlichkeiten der realen Welt) zu bestimmen ist. Anschaulich bedeutet dies: Der aktuelle Wert eines Finanzinstruments wird einzig und alleine durch Arbitragefreiheit festgelegt und NICHT durch die Meinung der Marktteilnehmer bzgl. zukuenftiger Marktentwicklungen.

• Stefan Tappe (Wirtschaftsuniversität Wien), Thursday, February 7, 2008, 18:15 Room 110 (first floor), Robert-Mayer-Str. 10, Faculty of Mathematics
  Title: Levy term structure models as solutions of infinite dimensional SDE's

  Term structure models driven by Levy processes have become an important subject in interest rate theory from mathematical finance. In this talk, we focus on Levy driven Heath, Jarrow and Morton (HJM) models with volatility structures depending on the prevailing forward curve. As we shall see, forward rate dependend volatilities make the model being a solution of an infinite dimensional SDE, which gives rise to discuss existence and uniqueness of solutions. There are several reasons why, in practice, one is interested in term structure models which admit a finite dimensional realization (FDR), that is the forward rate process proceeds on a finite dimensional submanifold. Using ideas from differential geometry, we shall characterize, in terms of the forward rate volatilities, those Levy driven HJM models possessing an FDR. As an application, we shall have a look at the existence of short rate realizations.

• Alexander Lindner (Technical University of Braunschweig), Friday, January 18, 2008, 16:15 Room 711 groß (seventh floor), Robert-Mayer-Str. 10, Faculty of Mathematics, talk in the Mathematical Colloquium.
  Title: Verallgemeinerte Ornstein-Uhlenbeck Prozesse

  Ein verallgemeinerter Ornstein-Uhlenbeck Prozess (V_t) ist gegeben als Lösung der stochastischen Differentialgleichung dV_t = V_{t-} dX_t + dY_t, wobei (X_t,Y_t) ein geeigneter bivariater Levyprozess ist. Zunächst werden einige Spezialfälle dieses Prozesses und Ihre Anwendungen in Finanz- und Vesicherungsmathematik vorgestellt. Danach wenden wir uns der Analyse solcher Prozesse zu und charakterisieren insbesondere, wann stationäre Lösungen existieren und welche Eigenschaften die stationäre Lösung besitzt. Der Vortrag beruht auf gemeinsamen Arbeiten mit Ross Maller und Ken-iti Sato.

• Hans-Peter Schmidli (University of Cologne), Friday, July 6, 2007, 17:45 Room 711 groß (seventh floor), Robert-Mayer-Str. 10, Faculty of Mathematics, talk in the Mathematical Colloquium.
  Title: Optimisation problems in non-life insurance
  Slides are available as pdf-file here

  In an insurance company decisions have to be taken all the time. Any decision is the solution to some optimisation problem, even though the problem usually is not explicitly formulated. We will first consider optimisation in discrete time and use Bellman's method for the solution. As an explicit example we consider the dividend problem introduced by De Finetti. In order to treat continuous time models we will use martingale methods and the Hamilton-Jacobi-Bellman equation. By the explicit example of minimising ruin probabilities via reinsurance we will explain how to obtain the equation and how to verify that the optimal ruin probability really solves the equation. Finally we will review some further optimisation problems that had been treated in the literature.

• Claudia Klüppelberg (Munich University of Technology), Friday, July 6, 2007, 16:15 Room 711 groß (seventh floor), Robert-Mayer-Str. 10, Faculty of Mathematics, talk in the Mathematical Colloquium.
  Title: On a Levy-driven continuous time GARCH model
  Slides are available as pdf-file here

  We introduce a continuous-time GARCH [COGARCH(1,1)] model which, driven by a single Levy noise process, exhibits the same second order properties as the discrete-time GARCH(1,1) model. Moreover, the COGARCH(1,1) model has heavy tails and clusters in the extremes. The second order structure of the COGARCH(1,1) model allows for some estimation procedure based on the ARMA(1,1) autocorrelation structure of the model and other moments. The model can be fitted to high-frequency data, and the statistical analysis also provides an estimator for the volatility.

• Tina Marquardt (Munich University of Technology), Thursday, June 21, 2007, 18:15 Room 110 (first floor), Robert-Mayer-Str. 10, Faculty of Mathematics
  Title: Long memory continuous-time series analysis using fractional Levy processes

  The definition and properties of ARMA processes are reviewed. Since discrete-time series are often obtained by observing a continuous-time process at a discrete sequence of observation times, it is natural to model the underlying process as a continuous-time series. For this reason continuous-time ARMA (CARMA) models are introduced, which involve autocorrelation functions that show an exponential decrease over time. Hence, ARMA and CARMA processes belong to the family of short memory models. However, several measurements in hydrology, turbulence, finance, economics or tele-communications show long memory behaviour in the sense that they seem to require models, whose autocorrelation functions decay much less quickly. In this talk the fractionally integrated CARMA (FICARMA) models will be introduced, which belong to a class of long memory continuous-time stationary processes whose autocorrelation functions converge to zero at a power law. In particular, we develop a new approach to generate long memory moving aveage models by defining the class of fractional Levy processes which leads to a generalization of fractional Brownian motion. We also study the second order properties, sample path properties and consider integrals with respect to fractional Levy processes.

• Suresh Sethi (University of Texas at Dallas), Tuesday, March 6, 2007, 17:15 Room 110 (first floor), Robert-Mayer-Str. 10, Faculty of Mathematics
  Optimal Consumption and Portfolio Decisions With Partially Observable Real Prices

  We consider the optimal consumption and portfolio investment problem of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket prices over time. Both the cases when the investor observes the consumption basket prices and when he receives noisy observations on those are treated. We derive the optimal policy and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases. The compositions of the funds in the two cases are the same, but in general the investor's allocations of his wealth into these funds will differ. However, in the particular case when the investor has CRRA utilities, his optimal investment allocations into these funds are the same in both cases (joint work with Alain Bensoussan and Jussi Keppo)

• Talk in the Mathematical Colloquium:
  Berthold Ströter (Vorstand der FORTIS Deutschland Lebensversicherungs AG), Friday, February 2, 2007, 16:15, Room 711 groß (7th floor), Robert-Mayer-Str. 10, Faculty of Mathematics
  Das Berufsbild des Aktuars
  pdf-file

  Der Vortrag stellt die Anforderungen an den als Aktuar tätigen Mathematiker in der Lebensversicherung dar, an typischen Beispielen wie Produktentwicklung, Embedded Value Berechnungen sowie Asset Liability Management werden die Aufgaben und die Verantwortung des Aktuars veranschaulicht. Auf neuere Entwicklungen, die das Berufsbild derzeit verändern und erweitern, wird im Vortrag eingegangen. Der Ausbildungsgang zum Aktuar der Deutschen Aktuar Vereinigung (DAV) wird kurz erläutert. Auf die im Sommersemester geplante Vorlesung ''Einführung in die Lebensversicherungsmathematik'' mit anschließender Möglichkeit eines Praktikums für die Hörer der Vorlesung wird ein Ausblick genommen.

• Anna Battauz (Universita Bocconi, Milano), January 23, 2007, 10:15 a.m., Room 711 klein (7th floor), Robert-Mayer-Str. 10, Faculty of Mathematics
  Multiperiod Arbitrage and the Marginal Utility of Optimal Intertemporal Wealth

  Given a class A of non-satiated investors with continuous and convex preferences, a one-period security market is viable if some agent in A finds an optimal trade. Harrison and Kreps (1979) show that viability is equivalent to the existence of linear pricing rules. Our first contribution is to extend Harrison and Kreps' result to the case of intertemporal consumption and preferences for intermediate consumption that may exhibit satiation, non-convexity and discontinuity. Then we show that the set of linear pricing rules is characterized in terms of agents' marginal utilities of optimal intertemporal wealth even if the marginal utility of consumption fails to exist, and hence the envelope condition equating the marginal utility of wealth to marginal utility of consumption cannot be invoked. Moreover we relate linear pricing functionals to state price densities and equivalent martingale measures (joint work with Fulvio Ortu and Marzia De Donno).

• Andreas Kyprianou (University of Bath), July 20, 2006, 5:15 p.m. (Room 711 groß, Robert-Mayer-Str. 10, Faculty of Mathematics)
  First passage of reflected strictly stable processes

• Christian-Oliver Ewald (University of Leeds), June 8, 2006, 5:00 p.m. (Room 711 groß, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Malliavin calculus

  Malliavin calculus has recently been applied very successfully in Mathematical Finance. In the talk I will present a (very) informal introduction into Malliavin calculus and discuss some of its main application, such as for example "Modeling of markets with asymmetric information in continuous time","Hedging","Calibration of stochastic volatility models", "Greeks" and more if the time permits it.

  Rolf Poulsen (University of Copenhagen), June 8, 2006, 6:15 p.m. (Room 711 groß, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Barrier Options and Their Static Hedges: Simple Derivations and Extensions
  Paper

• Matthias Fengler (Sal. Oppenheim), May 19, 2005, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics

  A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a severe modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.

  
  

• Vicky Fasen (Munich University of Technology), May 19, 2005, 5:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Extremes of Subexponential Levy Driven Moving Average Processes
  

  In this talk we study the extremal behavior of a stationary continuous-time moving average process $Y(t)=\int_{-\infty}^{\infty}f(t-s)\,dL(s)$ for $t\in \R$ where f is a deterministic function and L is a Levy process whose increments, represented by L(1), are subexponential. We show that large jumps of the Levy process in combination with extremes of f cause excesses of Y and thus properly chosen discrete-time points are sufficient to specify the extremal behavior of the continuous-time process. The extremal behavior of Y is completely described by a weak limit of marked point processes. A complementary result guarantees the convergence of running maxima of Y.

• Anne Gundel (HU Berlin), May 12, 2005, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Utility Maximization under Model Uncertainty with a Shortfall Risk Constraint
  We consider the problem of utility maximization under model uncertainty. Instead of a single model or probability measure for future market events we take a whole set of measures and then maximize a utility functional which is robust with respect to this model uncertainty. The usual constraint is a cost limit. We will add a second constraint of bounded shortfall risk or expected loss. We will give a characterization of the solution to this utility maximization problem by means of its dual problem, the minimization of a certain convex functional. We will do this for an incomplete market. This is a joint work with Stefan Weber.

• Christian Fries, March 3, 2005, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  The (Cross-Currency) Markov Functional Model in Theory and Practice. Ein hybrides LIBOR Zinsmodell als Backward Algorithmus zur Bewertung komplexer/hybrider Zinsderivate
  

• Ludger Rüschendorf (University of Freiburg), October 28, 2004, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  On Ordering results for option prices
  

• Pavel Gapeev (Russian Academy of Sciences), September 16, 2004, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Optimal Stopping in Jump-Diffusion Models

  We present closed form solutions to some optimal stopping problems for jump-diffusion processes. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems where the smooth-fit principle may break down and then be replaced by the principle of continuous fit. The results can be interpreted as pricing perpetual American options on jump-diffusion markets.
  

• Stefan Ankirchner (TU Berlin), June 24, 2004, 6:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Additional utility of insiders in financial markets and information theory

  We consider a financial market model with two kinds of traders: Beside regular traders there are insiders whose extra information is respresented by some enlarged filtration. We present a method how to calculate the additional utility, i.e. the difference of the expected utility of an insider and the expected utility of a regular trader. The information drift, i.e. the drift one has to eliminate in order to preserve the martingale property, turns out to be the crucial quantity. We derive representations of information drifts for general enlargements of filtrations and discuss some general properties. In the second part we will show that information theory can be used in a very natural way in order to calculate the additional utility. We prove that in a complete market the additional logarithmic utility can be respresented in terms of the Shannon information. For general markets we provide some estimates and, finally, we give some examples. This is joint work with Steffen Dereich and Peter Imkeller.
  

• David Bates (University of Iowa und NBER), June 18, 2004, 10:00 p.m. (Room 308 B, Department of Economics, Mertonstr. 17-21)
  Maximum Likelihood Estimation of Latent Affine Processes

• Francesca Biagini (University of Bologna), Friday , June 4, 2004, 4:00 p.m. s.t. (Room 110 , Robert-Mayer-Str. 10, Faculty of Mathematics)
  Minimal Variance Hedging for Insider Trading

  In this paper we first study the problem of minimal hedging for an insider trader in incomplete markets. We use the forward integral in order to model the insider portfolio and consider a general larger filtration. We characterise the optimal strategy in terms of a martingale condition. In the second part we focus on a problem of mean-variance hedging where the insider tries to minimise the variance of his wealth at time T given that this wealth has a fixed expected value A. We solve this problem for an initial enlargement of filtration by providing an explicit solution (joint work with Bernt Oksendal)

• Jan 22, 2004, 6:15 - 7:15 p.m. (Room 110, Robert-Mayer-Str. 10, Faculty of Mathematics)
  Malte Sieveking (FB Mathematik, Goethe-Universität Frankfurt)
  Kreditwürdigkeit: Beispiel für ökonomische Mathematik