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

Dolinsky, Yan

Electron. Commun. Probab. 19, Paper No. 19, 11 p. (2014).

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 \(\mathbb R^N\).

Reviewer: Yuri Kifer (Jerusalem)

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