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Game options in an imperfect market with default

Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès (2017), Game options in an imperfect market with default, SIAM Journal on Financial Mathematics, 8, 1, p. 532–559. 10.1137/16M1109102

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
SIAM Journal on Financial Mathematics
Volume
8
Number
1
Publisher
Society for Industrial and Applied Mathematics
Pages
532–559
Publication identifier
10.1137/16M1109102
Metadata
Show full item record
Author(s)
Dumitrescu, Roxana
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Quenez, Marie-Claire
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Sulem, Agnès
INRIA Rocquencourt
Abstract (EN)
We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Yuri Kifer in the case of a perfect market model to the case of an imperfect market with default, when the imperfections are taken into account via the nonlinearity of the wealth dynamics. We introduce the seller's price of the game option as the infimum of the initial wealths which allow the seller to be superhedged.We prove that this price coincides with the value function of an associated generalized Dynkin game expressed with a nonlinear expectation induced by a nonlinear BSDE with default jump. We moreover study the existence of superhedging strategies. We then address the case of ambiguity on the model, - for example ambiguity on the default probability - and characterize the robust seller's price of a game option as the value function of a {\em mixed generalized} Dynkin game. We study the existence of a cancellation time and a trading strategy which allow the seller to be super-hedged, whatever the model is.
Subjects / Keywords
Game options; imperfect markets; generalized Dynkin games; nonlinearexpectations; backward stochastic differential equations; nonlinear pricing; doubly reflected backward stochastic differential equations

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