Solving the dual Russian option problem by using change-of-measure arguments

We apply the change-of-measure arguments of Shepp and Shiryaev (Theory of Probability and its Applications, 1994, 39, 103–119) to study the dual Russian option pricing problem proposed by Shepp and Shiryaev (Probability Theory and Mathematical Statistics: Lectures presented at the semester held in St. Peterburg, Russia, March 2 April 23, 1993, Amsterdam, the Netherlands: Gordon and Breach, 1996, pp. 209–218) as an optimal stopping problem for a one-dimensional diffusion process with reflection. We recall the solution to the associated free-boundary problem and give a solution to the resulting one-dimensional optimal stopping problem by using the martingale approach of Beibel and Lerche (Statistica Sinica, 1997, 7, 93–108) and (Theory of Probability and its Applications, 2000, 45, 657–669).