Robust mean-variance stochastic differential reinsurance and investment games under volatility risk and model uncertainty

Guohui Guan, Zongxia Liang and Yi Xia

Papers from arXiv.org

Abstract: This paper investigates robust stochastic differential games among insurers under model uncertainty and stochastic volatility. The surplus processes of ambiguity-averse insurers (AAIs) are characterized by drifted Brownian motion with both common and idiosyncratic insurance risks. To mitigate these risks, AAIs can purchase proportional reinsurance. Besides, AAIs allocate their wealth in a financial market consisting of cash, and a stock characterized by the 4/2 stochastic volatility model. AAIs compete with each other based on relative performance with the mean-variance criterion under the worst-case scenario. This paper formulates a robust time-consistent mean-field game in a non-linear system. The AAIs seek robust, time-consistent response strategies to achieve Nash equilibrium strategies in the game. We introduce $n$-dimensional extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations and corresponding verification theorems under compatible conditions. Semi-closed forms of the robust $n$-insurer equilibrium and mean-field equilibrium are derived, relying on coupled Riccati equations. Suitable conditions are presented to ensure the existence and uniqueness of the coupled Riccati equation as well as the integrability in the verification theorem. As the number of AAIs increases, the results in the $n$-insurer game converge to those in the mean-field game. Numerical examples are provided to illustrate economic behaviors in the games, highlighting the herd effect of competition on the AAIs.

Date: 2024-12
New Economics Papers: this item is included in nep-gth, nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2412.09171 Latest version (application/pdf)

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:arx:papers:2412.09171

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().