Statistics Papers

Document Type

Journal Article

Date of this Version

1995

Publication Source

Theory of Probability & Its Applications

Volume

39

Issue

1

Start Page

103

Last Page

119

DOI

10.1137/1139004

Abstract

The “Russian option” was introduced and calculated with the help of the solution of the optimal stopping problem for a two-dimensional Markov process in [10]. This paper proposes a new derivation of the general results [10]. The key idea is to introduce the dual martingale measure which permits one to reduce the “two-dimensional” optimal stopping problem to a “one-dimensional” one. This approach simplifies the discussion and explain the simplicity of the answer found in [10].

Copyright/Permission Statement

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

diffusion model of the (B, S)-market, bank account, rational option price, rational expiration time, optimal stopping rules, smooth sewing condition, the Stephan problem, diffusion with reflection

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Date Posted: 27 November 2017

This document has been peer reviewed.