Paper: arXiv 2511.12292

Authors: Bohan Li, Wenyuan Li, Kenneth Tsz Hin Ng, Sheung Chi Phillip Yam

Abstract

A mutual insurance company (MIC) is a type of consumer cooperative owned by its policyholders. By purchasing insurance from an MIC, policyholders effectively become member-owners of the company and are entitled to a share of the surplus, which is determined by their own collective claims and premium contributions. This sharing mechanism creates an interactive environment in which individual insurance strategies are influenced by the actions of others. Given that mutual insurers account for nearly one-third of the global insurance market, the analysis of members’ behavior under such a sharing mechanism is of both practical and theoretical importance. This article presents a first dynamic study of members’ behavior in the prevalent mutual insurance market under the large-population limit. With members’ wealth processes depending on the law of the insurance strategies, we model the surplus-sharing mechanism using an extended mean field game (MFG) framework and address the fundamental question of how strategic interactions in this setting influence individual decisions. Mathematically, we establish the global-in-time existence and uniqueness of the mean field forward-backward stochastic differential equation (MF-FBSDE) characterizing the Nash equilibrium strategy, employing techniques to accommodate realistic insurance constraints. Computationally, we develop a modified deep BSDE algorithm capable of solving the extended MFG problem with an additional fixed-point structure on the control. Utilizing this scheme, we examine how structural features of the MIC’s design, such as the composition of risk classes and surplus-sharing proportions, reshape members’ decisions and wealth through collective interactions, underscoring the central role of these mechanisms in MICs.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated mathematical framework utilizing Extended Mean Field Games and MF-FBSDEs to model mutual insurance interactions. However, its focus is strictly theoretical and computational (via Deep BSDE neural network solvers) without empirical testing on real-world insurance claim datasets.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze Strategic Interactions & Wealth Dynamics in Mutual Insurance Markets"] --> B["Data/Inputs: Policyholder Wealth Processes, Risk Class Compositions, Surplus-Sharing Ratios & Insurance Constraints"]
    B --> C["Methodology: Formulate Extended Mean Field Game (MFG) Framework with Mean Field FBSDE"]
    C --> D["Theoretical Proof: Establish Global-in-time Existence & Uniqueness of Nash Equilibrium"]
    D --> E["Computational Process: Solve Extended MFG using Modified Deep BSDE Algorithm with Control Fixed-Point Structure"]
    E --> F["Key Outcomes: Demonstrate How Surplus-Sharing Ratios & Risk Class Design Reshape Individual Strategies & Wealth"]

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0 of 74 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.