Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions

2016/06/14 by Masaaki Fujii, Fujii, Masaaki, Akihiko Takahashi +1
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paper · pdf · doi:10.48550/arxiv.1606.04285

Forthcoming in Stochastic Processes and their Applications

arxiv created 2018/05/23 · arxiv updated 2018/05/24

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.

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