# American Institute of Mathematical Sciences

September  2021, 17(5): 2703-2714. doi: 10.3934/jimo.2020090

## Lookback option pricing problem of mean-reverting stock model in uncertain environment

 1 School of Mathematics, Renmin University of China, Beijing 100872, China 2 School of Information Technology & Management, University of International, Business & Economics, Beijing 100029, China 3 School of Economics & Management, Beijing University of Chemical, Technology, Beijing 100029, China

* Corresponding author: Xiangfeng Yang

Received  February 2019 Revised  January 2020 Published  September 2021 Early access  May 2020

Fund Project: The second author is supported by the Program for Young Excellent Talents in UIBE (No.18YQ06).

A lookback option is an exotic option that allows investors to look back at the underlying prices occurring over the life of the option, and to exercise the right at assets optimal point. This paper proposes a mean-reverting stock model to investigate the lookback option in an uncertain environment. The lookback call and put options pricing formulas of the stock model are derived, and the corresponding numerical algorithms are designed to compute the prices of these two options.

Citation: Miao Tian, Xiangfeng Yang, Yi Zhang. Lookback option pricing problem of mean-reverting stock model in uncertain environment. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2703-2714. doi: 10.3934/jimo.2020090
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##### References:
Lookback call option price $f_{call}$ with different parameters
Lookback put option price $f_{put}$ with different parameters