Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game
This article describes a class of jump-uncertain stochastic control systems, and derives an Itô–Liu formula with jump. We characterize an optimal control law, that satisfies the Hamilton–Jacobi–Bellman equation with jump. Then, this paper deduces the optimal portfolio game under uncertain stochastic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1885 |
| _version_ | 1797482015723880448 |
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| author | Chengyu Wu Lu Yang Chengke Zhang |
| author_facet | Chengyu Wu Lu Yang Chengke Zhang |
| author_sort | Chengyu Wu |
| collection | DOAJ |
| description | This article describes a class of jump-uncertain stochastic control systems, and derives an Itô–Liu formula with jump. We characterize an optimal control law, that satisfies the Hamilton–Jacobi–Bellman equation with jump. Then, this paper deduces the optimal portfolio game under uncertain stochastic financial markets with jump. The information of players is symmetrical. The financial market is constituted of a risk-free asset and a risky asset whose price process is subjected to the jump-uncertain stochastic Black–Scholes model. The game is formulated by two utility maximization problems, each investor tries to maximize his relative utility, which is the weighted average of terminal wealth difference between his terminal wealth and that of his competitor. Finally, the explicit expressions of equilibrium investment strategies and value functions for the constant absolute risk-averse and constant relative risk-averse utility function are derived by using the dynamic programming principle. |
| first_indexed | 2024-03-09T22:22:15Z |
| format | Article |
| id | doaj.art-7d0bd42858f84accbf2e7108e9e5fc1c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:15Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7d0bd42858f84accbf2e7108e9e5fc1c2023-11-23T19:12:34ZengMDPI AGSymmetry2073-89942022-09-01149188510.3390/sym14091885Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio GameChengyu Wu0Lu Yang1Chengke Zhang2School of Management, Guangdong University of Technology, Guangzhou 510520, ChinaSchool of Management, Guangdong Polytechnic Normal University, Guangzhou 510665, ChinaSchool of Economics and Commence, Guangdong University of Technology, Guangzhou 510520, ChinaThis article describes a class of jump-uncertain stochastic control systems, and derives an Itô–Liu formula with jump. We characterize an optimal control law, that satisfies the Hamilton–Jacobi–Bellman equation with jump. Then, this paper deduces the optimal portfolio game under uncertain stochastic financial markets with jump. The information of players is symmetrical. The financial market is constituted of a risk-free asset and a risky asset whose price process is subjected to the jump-uncertain stochastic Black–Scholes model. The game is formulated by two utility maximization problems, each investor tries to maximize his relative utility, which is the weighted average of terminal wealth difference between his terminal wealth and that of his competitor. Finally, the explicit expressions of equilibrium investment strategies and value functions for the constant absolute risk-averse and constant relative risk-averse utility function are derived by using the dynamic programming principle.https://www.mdpi.com/2073-8994/14/9/1885jump-uncertain stochastic differential equationthe optimal equation of jump-uncertain stochastic processportfolio game under symmetry informationpower utilityexponential utility |
| spellingShingle | Chengyu Wu Lu Yang Chengke Zhang Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game Symmetry jump-uncertain stochastic differential equation the optimal equation of jump-uncertain stochastic process portfolio game under symmetry information power utility exponential utility |
| title | Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game |
| title_full | Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game |
| title_fullStr | Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game |
| title_full_unstemmed | Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game |
| title_short | Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game |
| title_sort | uncertain stochastic optimal control with jump and its application in a portfolio game |
| topic | jump-uncertain stochastic differential equation the optimal equation of jump-uncertain stochastic process portfolio game under symmetry information power utility exponential utility |
| url | https://www.mdpi.com/2073-8994/14/9/1885 |
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