Teaching / Enseignment

Programmation dynamique (ENSAE, 2017)

Description du cours: 

Ce cours a pour objectif d’introduire les principaux outils de base en programmation dynamique en restant dans un cadre déterministe et en insistant sur les applications économiques. Nous traiterons dans un premier temps du temps discret en horizon fini puis infini. Nous aborderons ensuite le temps continu avec le calcul des variations et une introduction au contrôle optimal en insistant sur l’approche programmation dynamique de Bellman. Certaines preuves seront juste ébauchées de manière heuristique sans que soit explicité en détail le cadre fonctionnel rigoureux.

Notes: 

Stochastic analysis in financial and actuarial mathematics 1 (TU Wien, 2022)

Subject of course: 

Definition and properties of multi-dimensional normal distribution, definition and elementary properties of Brownian motion, existence and Hölder continuity of Brownian motion using the Kolmogorov-Chentsov continuity criterion, filtrations, stopping times, progressive measurability, path properties, martingales, uniform integrability, Vitali's convergence theorem, sub- and supermartingales, maximum inequality, Doob's inequality for p-integrable submartingales, Doob's optional sampling theorem with applications, local martingales and examples, integration of predictable step processes, p-variation of functions, quadratic variation and covariation process of continuous local martingales, Kunita-Watanabe inequality, stochastic integration for continuous local martingales and generalization for continuous semimartingales, chain rule and convergence theorems for stochastic integrals (with respect to continuous semimartingales), integration by parts, multi-dimensional Ito formula with applications, Tanaka's formula, local Ito formula and Ito formula for holomorphic functions.

Documents: 

Slides: [PDF]

Optimal Control and Backward Stochastic Differential Equations (TU Wien, 2019)

Subject of course: 

Monte-Carlo Methods (TU Wien, 2021)

Subject of course: 

Monte-Carlo methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results of the problems which are difficult or impossible to solve analytically. We focus on the following topics in this course.

Exercises and solutions: 

Machine Learning in Finance (TU Wien, 2020, 2022)

Subject of course

After successful completion of the course, students are able to explain how Machine Learning works and how it is applied to mathematical problems in finance. In particular, the students are able to

Materials:

Finanzmathematik 1: disktrete Modelle (TU Wien, 2018-2023)

Inhalt der Lehrveranstaltung: 

Ein-Periodenmodell (Arbitrage, risikoneutrales Maß, Bewertung von Claims, Vollständigkeit, Sub-/Superhedging, optimale Portfolios) Mehrperiodenmodell in diskreter Zeit (selbstfinanzierende Handelsstrategien, Satz von Dalang/Morton/Willinger) Binomialmodell, Verteilung des Maximums, Grenzübergang im Binomialmodell, Black-Scholes Modell, Amerikanische Optionen, Snell'sche Einhüllende, Doob'sche Zerlegung

Unterlagen:

Die Vorlesung basiert auf dem Buch „Stochastic Finance: an Introduction in Discrete Time“ von Föllmer und Schied. 

https://www.degruyter.com/document/doi/10.1515/9783110218053/html 

Vorlesungsnotizen:  

Zinsstrukturmodelle und -derivate (TU Wien, 2018-2020)

Inhalt der Lehrveranstaltung