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Numerical algorithms for reflected anticipated backward stochastic differential equations with two obstacles and default risk

 
: Wang, J.; Korn, R.

:
Volltext ()

Risks 8 (2020), Nr.3, Art. 72, 30 S.
ISSN: 2227-9091
Englisch
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer ITWM ()

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.

: http://publica.fraunhofer.de/dokumente/N-602482.html