Anthony Reveillac (HU):Representation formula for BSDEs driven by continuous Markov martingales & Regulatory Capital Processes

In this talk we consider quadratic growth BSDE driven by continuous local martingales. First we derive the Markov property of a forward-backward system when the driving martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. It enables us to obtain the main result of this talk that is to describe the control process of the BSDE in terms of a differential operator of the solution process and the correlation coefficient of the forward process. This formula generalizes the results obtained by several authors in the Brownian setting, designed to represent the optimal delta hedge in the context of cross hedging insurance derivatives that generalizes the derivative hedge in the Black-Scholes model. It involves Malliavin's calculus which is not available in the general martingale setting. Consequently, we propose a new method based on stochastic calculus techniques. This is a joint work with Peter Imkeller and Anja Richter.