Geodesic
On the Russian option: The expected waiting time
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 564-575

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In the context of the Russian option of L. Shepp and A. N. Shiryaev, we present a new derivation of the solution for the underlying one-dimensional optimal stopping problem. Our method is not based on the smooth pasting guess and Ito formula, but only uses the strong Markov property. In addition, the exact formula is given for the expected waiting time of the optimal stopping strategy. Two different methods for this computation are presented. Both methods can be easily generalized to treat similar problems for general one-dimensional time-homogeneous diffusions.
Keywords: Russian option, infinitesimal operator, instantaneous reflection, the expected waitingtime, Markov process, the strong Markov property, Black–Scholes model, geometric Brownian motion, optimal stopping (strategy), payoff, the gainfunction, discounting, smooth pasting, Girsanov's change of measure.
Mots-clés : Cauchy type equation, diffusion 
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     author = {S. Graversen and G. Peskir},
     title = {On the {Russian} option: {The} expected waiting time},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a7/}
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S. Graversen; G. Peskir. On the Russian option: The expected waiting time. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 564-575. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a7/