Paper: arXiv 2412.09157

Authors: Guohui Guan, Zongxia Liang, Yi Xia

Abstract

This paper studies the robust reinsurance and investment games for competitive insurers. Model uncertainty is characterized by a class of equivalent probability measures. Each insurer is concerned with relative performance under the worst-case scenario. Insurers’ surplus processes are approximated by drifted Brownian motion with common and idiosyncratic insurance risks. The insurers can purchase proportional reinsurance to divide the insurance risk with the reinsurance premium calculated by the variance principle. We consider an incomplete market driven by the 4/2 stochastic volatility mode. This paper formulates the robust mean-field game for a non-linear system originating from the variance principle and the 4/2 model. For the case of an exponential utility function, we derive closed-form solutions for the $n$-insurer game and the corresponding mean-field game. We show that relative concerns lead to new hedging terms in the investment and reinsurance strategies. Model uncertainty can significantly change the insurers’ hedging demands. The hedging demands in the investment-reinsurance strategies exhibit highly non-linear dependence with the insurers’ competitive coefficients, risk aversion and ambiguity aversion coefficients. Finally, numerical results demonstrate the herd effect of competition.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining robust mean-field games, stochastic volatility (4/2 model), and robust control theory under model uncertainty. However, it is entirely theoretical and lacks real-world empirical backtesting or data validation beyond basic numerical simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Formulate & solve robust reinsurance-investment game under model uncertainty] --> B[Inputs: 4/2 Stochastic Volatility, Variance Premium Principle, Relative Concerns]
    B --> C[Methodology: Formulate N-insurer game & Mean-Field Game MFG with exponential utility]
    C --> D[Computation: Derive closed-form solutions via Hamilton-Jacobi-Bellman HJB equations]
    D --> E[Outcomes: Identify new hedging terms, herd effects, & non-linear strategy dependencies]

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3 of 115 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.