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

Clicks: 166
ID: 110909
2020
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.
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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

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