Solving the dual Russian option problem by using change‐of‐measure arguments. Issue 2 (6th April 2019) - Gapeev, Pavel V.
Abstract: 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).