A Free Boundary Problem Arising from a Multi-state Regime-switching Stock Trading Model

Chonghu Guan; Jing Peng; Zuo Quan Xu

doi:10.1016/j.jde.2022.08.006

A Free Boundary Problem Arising from a Multi-state Regime-switching Stock Trading Model

Chonghu Guan, Jing Peng, Zuo Quan Xu

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C^∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.

Original language	English
Pages (from-to)	436-459
Number of pages	24
Journal	Journal of Differential Equations
Volume	337
DOIs	https://doi.org/10.1016/j.jde.2022.08.006
Publication status	Published - 15 Nov 2022

Keywords

Free boundary problem
Regime-switching
Stock trading
System of parabolic variational inequalities

ASJC Scopus subject areas

Analysis
Applied Mathematics

More information

10.1016/j.jde.2022.08.006

http://hdl.handle.net/10397/97208

Cite this

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title = "A Free Boundary Problem Arising from a Multi-state Regime-switching Stock Trading Model",

abstract = "In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.",

keywords = "Free boundary problem, Regime-switching, Stock trading, System of parabolic variational inequalities",

author = "Chonghu Guan and Jing Peng and Xu, {Zuo Quan}",

note = "Funding Information: This author is partially supported by NSF of Guangdong Province of China (No. 2021A1515012031 and No. 2022A1515010263), NSFC (No. 11901244).The author acknowledges financial support from NSFC (No. 11971409).The author acknowledges financial support from NSFC (No. 11971409), The Hong Kong RGC (GRF No. 15202421), The PolyU-SDU Joint Research Center on Financial Mathematics and the CAS AMSS-POLYU Joint Laboratory of Applied Mathematics, The Hong Kong Polytechnic University. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

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N1 - Funding Information: This author is partially supported by NSF of Guangdong Province of China (No. 2021A1515012031 and No. 2022A1515010263), NSFC (No. 11901244).The author acknowledges financial support from NSFC (No. 11971409).The author acknowledges financial support from NSFC (No. 11971409), The Hong Kong RGC (GRF No. 15202421), The PolyU-SDU Joint Research Center on Financial Mathematics and the CAS AMSS-POLYU Joint Laboratory of Applied Mathematics, The Hong Kong Polytechnic University. Publisher Copyright: © 2022 Elsevier Inc.

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N2 - In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.

AB - In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.

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KW - Stock trading

KW - System of parabolic variational inequalities

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A Free Boundary Problem Arising from a Multi-state Regime-switching Stock Trading Model

Abstract

Keywords

ASJC Scopus subject areas

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