Loading...
Malliavin calculus for backward stochastic differential equations and applications to numerical solutions
Hu, Yaozhong Nualart, David Song, Xiaoming
Hu, Yaozhong
Nualart, David
Song, Xiaoming
Citations
Altmetric:
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/11-AAP762.
Date
2011-04-01
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Backward stochastic differential equations, Malliavin calculus, explicit scheme, implicit scheme, Clark–Ocone–Haussman formula, rate of convergence, Hölder continuity of the solutions
Citation
Hu, Yaozhong., Nualart, David., Song, Xiaoming. "Malliavin calculus for backward stochastic differential equations and applications to numerical solutions." Ann. Appl. Probab. Volume 21, Number 6 (2011), 2379-2423. http://dx.doi.org/10.1214/11-AAP762.