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

2025-02-08

AI Summary

This paper investigates dynamic reinsurance design under mean-variance preferences in the presence of belief heterogeneity between an insurer and a reinsurer, introducing incentive-compatibility constraints—jointly and for the first time—to mitigate moral hazard. Building upon the Cramér–Lundberg risk model augmented with risk-free asset investment, we extend the Hamilton–Jacobi–Bellman (HJB) equation and employ region-wise optimization to derive closed-form equilibrium strategies and a nonstandard reinsurance contract structure—distinct from conventional proportional or excess-of-loss forms. Theoretically, belief divergence is shown to fundamentally reshape optimal reinsurance arrangements; our model exhibits superior robustness and empirical plausibility compared to benchmarks assuming homogeneous beliefs or omitting incentive constraints. Numerical experiments confirm the sensitivity of derived strategies to key parameters and demonstrate strong practical applicability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 Cram'er-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.

Problem

• Dynamic reinsurance design under heterogeneous beliefs and mean-variance
• Solving extended HJB system with partitioned domain optimization technique
• Comparing optimal contracts with homogeneous belief models

Innovation

• Dynamic reinsurance design with heterogeneous beliefs
• Partitioned domain optimization technique application
• Incentive compatibility constraint addressing moral hazard