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

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

2012-02-21

arxiv.org/abs/1202.4625v1

Annals of Applied Probability 2011, Vol. 21, No. 6, 2379-2423

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/11-AAP762 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/11-AAP762

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.

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