Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Malliavin calculus for backward stochastic differential equations and application for numerical solutions

Tuesday, December 13, 2011 at 11:30am - 12:30pm

Speaker: Xiaoming Song, University of North Carolina

In this paper, we study backward stochastic differential equations with general terminal value and general random generator. In particular, we don't require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation neither. Motivated from applications to numerical simulations, first we obtain the $L^p$-H"older continuity of the solution. Then, we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained $L^p$-H"older continuity results. The main tool is the Malliavin Calculus.

Speaker: Xiaoming Song, University of North Carolina

Location   Hill 705