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)

Masaaki Fujii and Akihiko Takahashi
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Masaaki Fujii: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo

No CARF-F-436, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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.

Pages: 42
Date: 2018-05
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