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

By Yaozhong Hu, David Nualart, Xiaoming Song. 2011

76 citations recorded by the source corpus.

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 $L^p$-H\"{o}lder 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\"{o}lder continuity results. The main tool is the Malliavin calculus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a02326453db782f09dc595989cd9d22baf96c97d

Citations in the corpus

• 7 – Backward Stochastic Differential Equations (2011, unknown): “[46] and Briand and Elie [11] for Lipschitz BSDEs and one-dimensional quadratic BSDEs.”