This article is cited in 15 papers

On the Russian option: The expected waiting time

S. Graversen, G. Peskir

Institute of Mathematics, University of Aarhus, Denmark

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.

Keywords: Russian option, infinitesimal operator, instantaneous reflection, the expected waitingtime, Cauchy type equation, Markov process, the strong Markov property, diffusion, Black–Scholes model, geometric Brownian motion, optimal stopping (strategy), payoff, the gainfunction, discounting, smooth pasting, Girsanov's change of measure.

Received: 05.03.1997

Language: English

DOI: 10.4213/tvp1953

 English version: Theory of Probability and its Applications, 1998, 42:3, 416–425

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