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Erscheinungsjahr: 
2020
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 3 [Article No.:] 72 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-30
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
numerical algorithm
reflected anticipated backward stochastic differential equations
discrete penalization scheme
discrete reflected scheme
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