Solving the dual Russian option problem by using change‐of‐measure arguments. Issue 2 (6th April 2019)

• Record Type: Journal Article
• Authors: Gapeev, Pavel V.
• Is Part Of: High frequency. Volume 2:Issue 2(2019)
• Page Start: 76
• Page End: 84
• Publication Date: 2019-04-06
• Subjects: Brownian motion -- change‐of‐variable formula with local time on surfaces -- diffusion process with reflection -- dual Russian option -- first hitting time -- free‐boundary problem -- martingale approach of Beibel and Lerche -- optimal stopping problem; Time-series analysis -- Periodicals; Big data -- Periodicals; Finance -- Statistical methods -- Periodicals; Mathematical models -- Periodicals; 519.55
• DOI: 10.1002/hf2.10030
• Languages: English
• ISSNs: 2470-6981

Abstract

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).