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

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  • Masaaki Fujii

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (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.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2018. "Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions," CIRJE F-Series CIRJE-F-1086, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2018cf1086
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2018/2018cf1086.pdf
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