Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions (Forthcoming in Stochastic Processes and their Applications) (Revised version of CARF-F-398)

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.