Work

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

Year: 2011

Type: article

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.

Source: The Annals of Applied Probability

DOI: 10.1214/11-aap762

Authors: Yaozhong Hu, David Nualart, Xiaoming Song

Institution: University of Kansas

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Stochastic Analysis of Gaussian Fractional Noises, Nonlinear Functionals of Fractional Brownian Motion