On the Russian Option: The Expected Waiting Time

Abstract

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.

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