Backward Stochastic Differential Equations and Applications to Mathematical Finance

The course is intended as an introduction to Backward Stochastic Differential Equations (BSDEs)

oriented towards applications in Mathematical Finance.

· BSDEs – the general results

· Existence and Uniqueness of Solution

· Comparison Principles

· Examples of Linear and Nonlinear BSDEs : applications to optimal control, 1-

dimensional BSDEs with non Lipschitz coefficients, e.g. with quadratic growth

generators, reflected BSDEs

· Forward-Backward Stochastic Differential Equations

· The Markovian Structure of FBSDEs

· The Feynman-Kac Formula and the Connection with Partial Differential Equations

· Coupled FBSDEs

· Applications

· Arbitrage-Free Pricing, Perfect Hedging and Superhedging

· Quadratic Pricing and Hedging