Articlebronze2011

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

45 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Numerical methods for differential equations Fuzzy Systems and Optimization

Abstract

In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not 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, either. Motivated from applications to numerical simulations, first we obtain the Lp-Hölder 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 Lp-Hölder continuity results. The main tool is the Malliavin calculus.

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References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme 2007Forward-Backward Stochastic Differential Equations and their Applications 2004Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations 2005A regression-based Monte Carlo method to solve backward stochastic differential equations 2004A numerical scheme for BSDEs 2007A forward scheme for backward SDEs

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