Discussion Papers 2016

CIRJE-F-1016	"Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions"
Author Name	Fujii, Masaaki and Akihiko Takahashi
Date	June 2016
Full Paper	PDF File
Remarks	Revised in June 2016 and November 2016; revised as CIRJE-F-1086.

Abstract
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expectations at each space-time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants
Keywords: asymptotic expansion, discretization, quadratic-growth BSDEs

Abstract

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expectations at each space-time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants

Keywords: asymptotic expansion, discretization, quadratic-growth BSDEs