# American Institute of Mathematical Sciences

• Previous Article
Optimal reinsurance and investment strategies for an insurer and a reinsurer under Hestons SV model: HARA utility and Legendre transform
• JIMO Home
• This Issue
• Next Article
Alliance strategy of construction and demolition waste recycling based on the modified shapley value under government regulation
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  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, doi: 10.3934/jimo.2020090
##### References:

show all references

##### References:
Lookback call option price $f_{call}$ with different parameters
Lookback put option price $f_{put}$ with different parameters
 [1] Weiwei Wang, Ping Chen. A mean-reverting currency model with floating interest rates in uncertain environment. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1921-1936. doi: 10.3934/jimo.2018129 [2] Edward Allen. Environmental variability and mean-reverting processes. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2073-2089. doi: 10.3934/dcdsb.2016037 [3] Hoi Tin Kong, Qing Zhang. An optimal trading rule of a mean-reverting asset. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1403-1417. doi: 10.3934/dcdsb.2010.14.1403 [4] Yanqing Hu, Zaiming Liu, Jinbiao Wu. Optimal impulse control of a mean-reverting inventory with quadratic costs. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1685-1700. doi: 10.3934/jimo.2018027 [5] Qihong Chen. Recovery of local volatility for financial assets with mean-reverting price processes. Mathematical Control & Related Fields, 2018, 8 (3&4) : 625-635. doi: 10.3934/mcrf.2018026 [6] Cuilian You, Le Bo. Option pricing formulas for generalized fuzzy stock model. Journal of Industrial & Management Optimization, 2020, 16 (1) : 387-396. doi: 10.3934/jimo.2018158 [7] Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. Ergodic control for a mean reverting inventory model. Journal of Industrial & Management Optimization, 2018, 14 (3) : 857-876. doi: 10.3934/jimo.2017079 [8] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065 [9] Zhuo Jin, Linyi Qian. Lookback option pricing for regime-switching jump diffusion models. Mathematical Control & Related Fields, 2015, 5 (2) : 237-258. doi: 10.3934/mcrf.2015.5.237 [10] Cuilian You, Yangyang Hao. Stability in mean for fuzzy differential equation. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1375-1385. doi: 10.3934/jimo.2018099 [11] Zhimin Liu, Shaojian Qu, Hassan Raza, Zhong Wu, Deqiang Qu, Jianhui Du. Two-stage mean-risk stochastic mixed integer optimization model for location-allocation problems under uncertain environment. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020094 [12] Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks & Heterogeneous Media, 2013, 8 (1) : 9-22. doi: 10.3934/nhm.2013.8.9 [13] Michael Grinfeld, Harbir Lamba, Rod Cross. A mesoscopic stock market model with hysteretic agents. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 403-415. doi: 10.3934/dcdsb.2013.18.403 [14] Sergey A. Suslov. Two-equation model of mean flow resonances in subcritical flow systems. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 165-176. doi: 10.3934/dcdss.2008.1.165 [15] Hayato Chiba, Georgi S. Medvedev. The mean field analysis of the Kuramoto model on graphs Ⅰ. The mean field equation and transition point formulas. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 131-155. doi: 10.3934/dcds.2019006 [16] Peng Zhang. Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 2019, 15 (2) : 537-564. doi: 10.3934/jimo.2018056 [17] Wenjia Jing, Olivier Pinaud. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5377-5407. doi: 10.3934/dcdsb.2019063 [18] Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591-608. doi: 10.3934/mbe.2013.10.591 [19] Alberto A. Pinto, Telmo Parreira. Localization and prices in the quadratic Hotelling model with uncertainty. Journal of Dynamics & Games, 2016, 3 (2) : 121-142. doi: 10.3934/jdg.2016006 [20] Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd. Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 553-576. doi: 10.3934/mbe.2012.9.553

2019 Impact Factor: 1.366
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32974332571029663, "perplexity": 9686.856653248926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655890092.28/warc/CC-MAIN-20200706011013-20200706041013-00038.warc.gz"}