9 August 2019
Selected Topics in the Theory of Backward Stochastic Differential Equations
1. Introduction, motivation
2. A short introduction to stochastic differential equations Existence and uniqueness (strong solutions), a priori estimate, examples (Black-Scholes model, etc.)
3. Backward stochastic differential equations Martingale representation property, a priori estimate, existence and uniqueness, comparison theorem
4. Markovian BSDEs and PDEs Markov property of BSDES, nonlinear Feynman-Kac’s formula
5. Introduction to quadratic BSDEs BMO martingales, Kobylanski’s result, unbounded case
6. SDEs and BSDEs with mean reflexion Introduction, existence and uniqueness, links with mean field PDEs
Lecturer: Philippe Briand (Université Savoie Mont Blanc, France)
Coordinator: Prof. Stefan Geiss
Jyväskylä Summer School offers courses to advanced Master's students, graduate students, and post-docs from the field of Mathematics and Science and Information Technology.
Prerequisites: Usual notions on measures, integration and probability theory. Brownian motion, Itô’s formula, notion on continuous time martingales and Markov processes.
Learning outcomes: The main objective of these lectures is to develop the theory of backward stochastic differential equations as introduced by Pardoux and Peng in 1990 which is now a standard tool of stochastic calculus. There is a lot of applications of this theory in particular to mathematical finance and to PDEs theory, as BSDEs provide a nonlinear version of the famous Feynman-Kac formula. In addition, recent developments of this theory are closely related to a recent and very active field of research namely mean field interactions.
EUR 0: Participation in the Summer School courses is free of charge, but students are responsible for covering their own meals, accommodation and travel costs as well as possible visa costs.
Jyväskylä Summer School is not able to grant Summer School students financial support.