## 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

### Keywords:

game options; model uncertainty; super-replication; Dynkin games
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