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Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk

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  • Jingnan Wang

    (Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany)

  • Ralf Korn

    (Department of Mathematics, University of Kaiserslautern, Fraunhofer ITWM, 67663 Kaiserslautern, Germany)

Abstract

We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.

Suggested Citation

  • Jingnan Wang & Ralf Korn, 2020. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk," Risks, MDPI, vol. 8(3), pages 1-30, July.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:72-:d:379252
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    References listed on IDEAS

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    8. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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