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Hedging of game options under model uncertainty in discrete time. (English) Zbl 1304.91216

The author derives a superreplication price for discrete-time game options under model uncertainty. As usual, the financial market consists here of a (non-risky) savings account and a risky asset (stock) whose price evolution is described by a sequence \(S_0,S_1,\dots,S_N\) but no a priori market probability is chosen and it is assumed only that \(0\leq a\leq |\ln S_{i+1} -\ln S_i|\leq b\). The author shows that the super-replication price is given by the supremum of Dynkin games values over a class of martingale measures with respect to the filtration generated by the coordinate process in \(\mathbb R^N\).

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
91G40 Credit risk
60G42 Martingales with discrete parameter
91A15 Stochastic games, stochastic differential games
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