Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-Term Expansions
41 Pages Posted: 16 Jun 2016 Last revised: 26 May 2018
Date Written: May 23, 2018
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, Lipschitz BSDEs, numerical scheme, BMO-martingales
JEL Classification: C61, C63
Suggested Citation: Suggested Citation