Optimal investment game for two regulated players with regime switching
This paper investigated a zero-sum stochastic investment game for two investors in a regime-switching market with common random time solvency regulations. We considered two types of intensities for the inter-arrival time of regulations: one was modeled as a function of a time-homogeneous Markov chai...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241651 |
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| author | Lin Xu Linlin Wang Hao Wang Liming Zhang |
| author_facet | Lin Xu Linlin Wang Hao Wang Liming Zhang |
| author_sort | Lin Xu |
| collection | DOAJ |
| description | This paper investigated a zero-sum stochastic investment game for two investors in a regime-switching market with common random time solvency regulations. We considered two types of intensities for the inter-arrival time of regulations: one was modeled as a function of a time-homogeneous Markov chain, while the other was treated as a deterministic function of time $ t $. In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. In the regime-switching model, players' optimal strategies resembled those in a non-regime-switching model but required dynamic adjustments based on the Markov chain state. In the second case, the associated HJBI equation was a parabolic PDE. We provided a numerical method using a Markov chain approximation scheme and presented several numerical examples to illustrate the impact of regime switching and random time solvency on optimal policies. |
| format | Article |
| id | doaj-art-4e2ae7a62fdb4dd49eba9e0068401a7c |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-4e2ae7a62fdb4dd49eba9e0068401a7c2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912346743470410.3934/math.20241651Optimal investment game for two regulated players with regime switchingLin Xu0Linlin Wang1Hao Wang2Liming Zhang3School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241002, ChinaSchool of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241002, ChinaSchool of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241002, ChinaSchool of Big Data and Statistics, Anhui University, Hefei, Anhui 230601, ChinaThis paper investigated a zero-sum stochastic investment game for two investors in a regime-switching market with common random time solvency regulations. We considered two types of intensities for the inter-arrival time of regulations: one was modeled as a function of a time-homogeneous Markov chain, while the other was treated as a deterministic function of time $ t $. In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. In the regime-switching model, players' optimal strategies resembled those in a non-regime-switching model but required dynamic adjustments based on the Markov chain state. In the second case, the associated HJBI equation was a parabolic PDE. We provided a numerical method using a Markov chain approximation scheme and presented several numerical examples to illustrate the impact of regime switching and random time solvency on optimal policies.https://www.aimspress.com/article/doi/10.3934/math.20241651stochastic investment gamesolvency regulationsfixed point methodmarkov chain approximation |
| spellingShingle | Lin Xu Linlin Wang Hao Wang Liming Zhang Optimal investment game for two regulated players with regime switching AIMS Mathematics stochastic investment game solvency regulations fixed point method markov chain approximation |
| title | Optimal investment game for two regulated players with regime switching |
| title_full | Optimal investment game for two regulated players with regime switching |
| title_fullStr | Optimal investment game for two regulated players with regime switching |
| title_full_unstemmed | Optimal investment game for two regulated players with regime switching |
| title_short | Optimal investment game for two regulated players with regime switching |
| title_sort | optimal investment game for two regulated players with regime switching |
| topic | stochastic investment game solvency regulations fixed point method markov chain approximation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241651 |
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