Game options in an imperfect market with default

Abstract : We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in the case of a perfect market model to the case of imperfections on the market taken into account via the nonlinearity of the wealth dynamics. In this framework, the pricing system is expressed as a nonlinear g-expectation/evaluation induced by a nonlinear BSDE with jump. We prove that the superhedging price of a game option coincides with the value function of a corresponding generalized Dynkin game expressed in terms of the g-evaluation, recently introduced in \cite{DQS2}. We then address the case of ambiguity on the model, - for example an ambiguity on the default probability -, and characterize the superhedging price of a game option as the value function of a mixed generalized Dynkin game. We prove the existence of a cancellation time and a trading strategy for the seller which allow him/her to be super-hedged, whatever the model is. This study is introduced by the analysis of the simpler case of American options.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.inria.fr/hal-01243603
Contributeur : Martine Verneuille <>
Soumis le : mardi 15 décembre 2015 - 11:07:33
Dernière modification le : mardi 11 octobre 2016 - 14:10:20

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Roxana Dumitrescu, Marie-Claire Quenez, Agnès Sulem. Game options in an imperfect market with default. 2015. <hal-01243603>

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