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

Jingnan Wang and Ralf Korn
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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

Risks, 2020, vol. 8, issue 3, 1-30

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.

Keywords: numerical algorithm; reflected anticipated backward stochastic differential equations; discrete penalization scheme; discrete reflected scheme (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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