Robust Optimal Reinsurance and Investment Problem Under Markov Switching via Actor–Critic Reinforcement Learning

Fang Jin (), Kangyong Cheng, Xiaoliang Xie and Shubo Chen
Additional contact information
Fang Jin: College of Science, Hunan City University, Yiyang 413000, China
Kangyong Cheng: College of Science, Hunan City University, Yiyang 413000, China
Xiaoliang Xie: College of Mathematics and Statistics, Hunan University of Technology and Business, Changsha 410215, China
Shubo Chen: College of Science, Hunan City University, Yiyang 413000, China

Mathematics, 2025, vol. 13, issue 21, 1-21

Abstract: This paper investigates a robust optimal reinsurance and investment problem for an insurance company operating in a Markov-modulated financial market. The insurer’s surplus process is modeled by a diffusion process with jumps, which is correlated with financial risky assets through a common shock structure. The economic regime switches according to a continuous-time Markov chain. To address model uncertainty concerning both diffusion and jump components, we formulate the problem within a robust optimal control framework. By applying the Girsanov theorem for semimartingales, we derive the dynamics of the wealth process under an equivalent martingale measure. We then establish the associated Hamilton–Jacobi–Bellman (HJB) equation, which constitutes a coupled system of nonlinear second-order integro-differential equations. An explicit form of the relative entropy penalty function is provided to quantify the cost of deviating from the reference model. The theoretical results furnish a foundation for numerical solutions using actor–critic reinforcement learning algorithms.

Keywords: robust optimal problem; reinsurance; investment; markov switching; actor–critic reinforcement learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3502/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3502/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3502-:d:1785621

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().