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

Masaaki Fujii and Akihiko Takahashi
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Masaaki Fujii: Faculty of Economics, The University of Tokyo
Akihiko Takahashi: Faculty of Economics, The University of Tokyo

No CIRJE-F-1086, CIRJE F-Series from CIRJE, Faculty of Economics, 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 pages
Date: 2018-05
New Economics Papers: this item is included in nep-his
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