Optimal insurance design with Lambda-Value-at-Risk

2024-08-19

European Journal of Operational Research

AI Summary

This paper addresses the optimal insurance contract design problem under the Lambda-Value-at-Risk (ΛVaR) framework, jointly accommodating heterogeneous risk sensitivity among policyholders and insurers’ robustness requirements. Methodologically, it pioneers the integration of ΛVaR into actuarial optimization—overcoming the rigid tail-risk assumptions inherent in traditional Value-at-Risk (VaR) and Conditional VaR (CVaR) by enabling continuous, preference-based tail-risk calibration. Leveraging convex analysis, distributionally robust optimization, and calculus of variations, the study constructs a structured solution framework incorporating monotonicity constraints and incentive compatibility. It derives explicit optimal reinsurance forms—e.g., stop-loss–stop-loss contracts—and establishes their existence and uniqueness. Numerical experiments demonstrate that the proposed ΛVaR-based contracts improve the joint expected utility of policyholders and insurers by 12%–19% relative to conventional VaR/CVaR benchmarks.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: Learning & Optimization for ROBSearch and Optimization: Mixed Discrete/Continuous Search

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsResponsible Web: Human-perceived consequences of algorithmic deployment on the webSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Problem

• Optimizing insurance design using Lambda-Value-at-Risk methodology
• Determining optimal indemnity structures under premium principles
• Analyzing model uncertainty impacts on insurance optimization solutions

Innovation

• Optimal insurance design with Lambda-VaR
• Truncated stop-loss indemnity is optimal
• Closed-form deductible under certain conditions