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

See all articles by Masaaki Fujii

Masaaki Fujii

University of Tokyo - Faculty of Economics

Akihiko Takahashi

University of Tokyo - Faculty of Economics

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

Fujii, Masaaki and Takahashi, Akihiko, Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-Term Expansions (May 23, 2018). Available at SSRN: https://ssrn.com/abstract=2795490 or http://dx.doi.org/10.2139/ssrn.2795490

Masaaki Fujii (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

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