L. A. Shepp, A. N. Shiryaev, “A new look at pricing of the “Russian Option””, Teor. Veroyatnost. i Primenen., 39:1 (1994), 130–149; Theory Probab. Appl., 39:1 (1994), 103

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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 1, Pages 130–149 (Mi tvp3764)

This article is cited in 96 scientific papers (total in 96 papers)

A new look at pricing of the “Russian Option”

L. A. Shepp^a, A. N. Shiryaev^b

^a AT&T Bell Laboratories, New Jersey, USA
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (888 kB) Citations (96)

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].

Keywords: diffusion model of the

(B, S)

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

Received: 05.07.1993

English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 1, Pages 103–119
DOI: https://doi.org/10.1137/1139004

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: L. A. Shepp, A. N. Shiryaev, “A new look at pricing of the “Russian Option””, Teor. Veroyatnost. i Primenen., 39:1 (1994), 130–149; Theory Probab. Appl., 39:1 (1994), 103–119

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp3764

https://www.mathnet.ru/eng/tvp/v39/i1/p130

This publication is cited in the following 96 articles:

Monir Chadad, Mohamed Erraoui, “Reflected stochastic differential equations driven by standard and fractional Brownian motion”, Stoch. Dyn., 24:02 (2024)
M. Çağlar, C. Vardar-Acar, “Stopping Levels for a Spectrally Negative Markov Additive Process”, Commun. Math. Stat., 2024
Pavel V. Gapeev, “Discounted optimal stopping zero-sum games in diffusion type models with maxima and minima”, Adv. Appl. Probab., 2024, 1
Wenyuan Wang, Ning Wang, Mi Chen, “On a doubly reflected risk process with running maximum dependent reflecting barriers”, Journal of Computational and Applied Mathematics, 422 (2023), 114880
Budhi Surya, Wenyuan Wang, Xianghua Zhao, Xiaowen Zhou, “Parisian excursion with capital injection for drawdown reflected Lévy insurance risk process”, Scandinavian Actuarial Journal, 2023:2 (2023), 97
M. Çağlar, A. Kyprianou, C. Vardar-Acar, “An optimal stopping problem for spectrally negative Markov additive processes”, Stochastic Processes and their Applications, 150 (2022), 1109
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba, José Carlos Dias, “GENERALIZED EXPONENTIAL BASIS FOR EFFICIENT SOLVING OF HOMOGENEOUS DIFFUSION FREE BOUNDARY PROBLEMS: RUSSIAN OPTION PRICING”, J Math Sci, 266:2 (2022), 353
Haoyang Cao, Xin Guo, “MFGs for partially reversible investment”, Stochastic Processes and their Applications, 150 (2022), 995
Pavel V. Gapeev, Peter M. Kort, Maria N. Lavrutich, Jacco J. J. Thijssen, “Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions”, Methodol Comput Appl Probab, 24:2 (2022), 789
Pavel V. Gapeev, “Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes”, Methodol Comput Appl Probab, 24:2 (2022), 749
Congjin Zhou, Guojing Wang, Jie Guo, “Optimal refinancing strategy for mortgage rate with regime switching”, Appl Stoch Models Bus & Ind, 38:1 (2022), 133
Pavel V. Gapeev, Hessah Al Motairi, “Discounted optimal stopping problems in first-passage time models with random thresholds”, J. Appl. Probab., 59:3 (2022), 714
Gapeev V P. Kort P.M. Lavrutich M.N., “Discounted Optimal Stopping Problems For Maxima of Geometric Brownian Motionswith Switching Payoffs”, Adv. Appl. Probab., 53:1 (2021), 189–219
Zhang X. Li L. Zhang G., “Pricing American Drawdown Options Under Markov Models”, Eur. J. Oper. Res., 293:3 (2021), 1188–1205
Wenyuan Wang, Xiaowen Zhou, “A Drawdown Reflected Spectrally Negative Lévy Process”, J Theor Probab, 34:1 (2021), 283
Zhongdi Cen, Anbo Le, “An efficient numerical method for pricing a Russian option with a finite time horizon”, International Journal of Computer Mathematics, 98:10 (2021), 2025
Gapeev V P., “Optimal Stopping Problems For Running Minima With Positive Discounting Rates”, Stat. Probab. Lett., 167 (2020), 108899
Min Hyeok Woo, Geon Ho Choe, “Pricing of American lookback spread options”, Stochastic Processes and their Applications, 130:10 (2020), 6300
Sören Christensen, Albrecht Irle, “The monotone case approach for the solution of certain multidimensional optimal stopping problems”, Stochastic Processes and their Applications, 130:4 (2020), 1972
Christensen S. Irle A., “A General Method For Finding the Optimal Threshold in Discrete Time”, Stochastics, 91:5 (2019), 728–753

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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