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

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ID: 110909
2020
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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.
Reference Key
wang2020risksnumerical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Jingnan Wang;Ralf Korn;Wang, Jingnan;Korn, Ralf;
Journal risks
Year 2020
DOI
10.3390/risks8030072
URL
https://doi.org/10.3390/risks8030072
Keywords
numerical algorithm reflected anticipated backward stochastic differential equations discrete penalization scheme discrete reflected scheme numerical algorithm reflected anticipated backward stochastic differential equations discrete penalization scheme discrete reflected scheme

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