Discussion Papers 2018

CIRJE-F-1086	"Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions"
Author Name	Fujii, Masaaki and Akihiko Takahashi
Date	May 2018
Full Paper	PDF File
Remarks	Forthcoming in Stochastic Processes and their Applications; revised version of CIRJE-F-1016

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.

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.