## Some calculations for Israeli options.(English)Zbl 1098.91055

The author describes the concept of an Israeli (or game) option introduced by Yu. Kifer [Finance Stoch. 4, No. 4, 443–463 (2000; Zbl 1066.91042)]. The pricing and hedging of these options is reduced to evaluating a saddle point problem associated with Dynkin games. In this paper two examples of perpetual Israeli options where solutions can be presented in the explicit form are demonstrated. The method of analysis is straightforward. The author guesses the form of the optimal stopping strategies using heuristic arguments based on fluctuation theory and then shows that the suggested solutions solve the associated saddle point problem. Martingale techniques are used. The Israeli $$\delta$$-penalty put and Russian options are considered and the solutions of the saddle point problem are presented for these cases. The paper is concluded with some remarks about Canadization and the finite expiry case.

### MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 60G40 Stopping times; optimal stopping problems; gambling theory 91A15 Stochastic games, stochastic differential games

Zbl 1066.91042
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