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BSDE Approach for Dynkin Game and American Game Option

  • El Hassan EssakyEmail author
  • M. Hassani
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 158)

Abstract

Consider a Dynkin game with payoff
$$ J(\lambda , {\upsigma }) = F\bigg [U_{\lambda }1_{\{\lambda< {\upsigma }\}} + L_{{\upsigma }}1_{\{\lambda > {\upsigma }\}}+ Q_{{\upsigma }}1_{\{ {\upsigma }=\lambda < T \}} + \xi 1_{\{ {\upsigma }= \lambda = T \}}\bigg ], $$
where \(F : \mathbb {R}\longrightarrow \mathbb {R}\) is a continuous nondecreasing function and \(\lambda , {\upsigma }\) are stopping times valued in [0, T]. We show the existence of a value as well as a saddle-point for this game using the theory of BSDE with double reflecting barriers. An American game option pricing problem is also discussed.

Keywords

Backward stochastic differential equations with double reflecting barriers Dynkin game Saddle-point American game option 

Mathematical Subject Classification 2010

60H10 60H20 60H30 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Département de Mathématiques et d’Informatique, Laboratoire de Modélisation et Combinatoire, Faculté Poly-disciplinaireUniversité Cadi AyyadSafiMorocco

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