Numerical computation for backward doubly SDEs with random terminal time

Matoussi Anis () and Sabbagh Wissal ()
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Matoussi Anis: University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Mathématiques, Avenue Olivier Messiaen, France
Sabbagh Wissal: University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Mathématiques, Avenue Olivier Messiaen, France

Monte Carlo Methods and Applications, 2016, vol. 22, issue 3, 229-258

Abstract: In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time τ. The main motivations are giving a probabilistic representation of the Sobolev’s solution of Dirichlet problem for semilinear SPDEs and providing the numerical scheme for such SPDEs. Thus, we study the strong approximation of this class of BDSDEs when τ is the first exit time of a forward SDE from a cylindrical domain. Euler schemes and bounds for the discrete-time approximation error are provided.

Keywords: Backward doubly stochastic differential equation; Monte Carlo method; Euler scheme; exit time; stochastic flow; SPDEs; Dirichlet condition (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0111

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