Dynamic reinsurance design with heterogeneous beliefs under the mean-variance framework

Paper: arXiv 2502.05474

Authors: Junyi Guo, Xia Han, Hao Wang

Abstract

This paper investigates the dynamic reinsurance design problem under the mean-variance criterion, incorporating heterogeneous beliefs between the insurer and the reinsurer, and introducing an incentive compatibility constraint to address moral hazard. The insurer’s surplus process is modeled using the classical Cramér-Lundberg risk model, with the option to invest in a risk-free asset. To solve the extended Hamilton-Jacobi-Bellman (HJB) system, we apply the partitioned domain optimization technique, transforming the infinite-dimensional optimization problem into a finite-dimensional one determined by several key parameters. The resulting optimal reinsurance contracts are more complex than the standard proportional and excess-of-loss contracts commonly studied in the mean-variance literature with homogeneous beliefs. By further assuming specific forms of belief heterogeneity, we derive the parametric solutions and obtain a clear optimal equilibrium solution. Finally, we compare our results with models where the insurer and reinsurer share identical beliefs or where the incentive compatibility constraint is relaxed. Numerical examples are provided to illustrate the impact of belief heterogeneity on optimal reinsurance strategies.

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 rigorous theoretical formulation using extended HJB systems, partitioned domain optimization, and continuous-time game theory to address dynamic reinsurance with belief heterogeneity. However, it is purely theoretical and numerical, lacking empirical backtests or real-world market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Dynamic Reinsurance Design under Mean-Variance Criterion with Heterogeneous Beliefs] --> B[Model Inputs: Surplus Process via Cramér-Lundberg Model & Risk-free Asset]
    B --> C[Formulate Optimization Problem with Incentive Compatibility Constraint]
    C --> D[Derive Extended Hamilton-Jacobi-Bellman HJB System]
    D --> E[Apply Partitioned Domain Optimization Technique]
    E --> F[Derive Parametric & Optimal Equilibrium Solutions]
    F --> G[Key Outcomes: Optimal contracts are more complex than standard proportional/excess-of-loss types]