Performance-based variable premium scheme and reinsurance design

2024-12-02

AI Summary

This paper addresses the incentive deficiency and risk imbalance arising from static reinsurance premium structures by proposing a performance-based variable premium mechanism: premiums are initially set stochastically and subsequently adjusted ex post—via bonuses or penalties—based on realized claims, thereby linking premiums to both the loss distribution and actual losses. Methodologically, we integrate risk measures, stochastic optimization, and Bowley bilateral bargaining theory to formulate an equilibrium model wherein the insurer selects an optimal reinsurance strategy subject to the reinsurer’s risk constraints, extending the Meyers–Chen actuarial pricing framework. Numerical experiments demonstrate that, compared with the conventional expected-value principle, our mechanism significantly reduces the reinsurer’s aggregate risk exposure while enhancing contract efficiency and incentive compatibility. To the best of our knowledge, this is the first systematic design embedding performance feedback directly into variable reinsurance pricing.

Technology Category

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

Application Category

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

Abstract

In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller's risk attitude. Building on the work of Meyers (1980) and Chen et al. (2016), we propose a new performance-based variable premium scheme for reinsurance policies, where the premium depends on both the distribution of the ceded loss and the actual realized loss. Under this scheme, the insurer and the reinsurer face a random premium at the beginning of the policy period. Based on the realized loss, the premium is adjusted into either a ''reward'' or ''penalty'' scenario, resulting in a discount or surcharge at the end of the policy period. We characterize the optimal reinsurance policy from the insurer's perspective under this new variable premium scheme. In addition, we formulate a Bowley optimization problem between the insurer and the monopoly reinsurer. Numerical examples demonstrate that, compared to the expected-value premium principle, the reinsurer prefers the variable premium scheme as it reduces the reinsurer's total risk exposure.

Problem

• Designing a performance-based variable reinsurance premium scheme
• Optimizing reinsurance policies considering random premium adjustments
• Comparing variable premium scheme with expected-value principle

Innovation

• Performance-based variable premium reinsurance scheme
• Premium adjusts based on realized loss outcomes
• Optimal reinsurance policy reduces risk exposure