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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Main Authors: Lin Xu, Linlin Wang, Hao Wang, Liming Zhang
Format: Article
Language:English
Published: AIMS Press 2024-12-01
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.
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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
work_keys_str_mv AT linxu optimalinvestmentgamefortworegulatedplayerswithregimeswitching
AT linlinwang optimalinvestmentgamefortworegulatedplayerswithregimeswitching
AT haowang optimalinvestmentgamefortworegulatedplayerswithregimeswitching
AT limingzhang optimalinvestmentgamefortworegulatedplayerswithregimeswitching