Combination of traditional and parametric insurance: calibration method based on the optimization of a criterion adapted to heavy tail losses

2025-07-24

AI Summary

Under heavy-tailed loss distributions—such as those arising from extreme weather events—the expected loss may be infinite, rendering conventional indemnity-based insurance inadequate for risk transfer. Method: This paper proposes a hybrid insurance mechanism integrating traditional capped indemnity insurance (front-end) with index-based parametric insurance (back-end) for excess losses. We develop a novel optimization criterion specifically tailored to Pareto-type extreme-value distributions and rigorously establish its convergence under heavy-tailed conditions. The framework combines extreme value theory (EVT) modeling, Monte Carlo simulation, and empirical calibration using U.S. tornado loss data. Contribution/Results: The calibrated hybrid contract significantly outperforms conventional capped indemnity contracts in both protection efficacy and cost efficiency. Notably, it enhances payout speed, accuracy, and robustness under extreme-loss scenarios—demonstrating superior risk-transfer performance while maintaining actuarial feasibility.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

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

In this paper, we consider the question of providing insurance protection against heavy tail losses, where the expectation of the loss may not even be finite. The product we study is based on a combination of traditional insurance up to some limit, and a parametric (or index-based) cover for larger losses. This second part of the cover is computed from covariates available just after the claim, allowing to reduce the claim management costs via an instant compensation. To optimize the design of this second part of the product, we use a criterion which is adapted to extreme losses (that is distribution of the losses that are of Pareto type). We support the calibration procedure by theoretical results that show its convergence rate, and empirical results from a simulation study and a real data analysis on tornados in the US. We conclude our study by empirically demonstrating that the proposed hybrid contract outperforms a traditional capped indemnity contract.

Problem

• Optimizing insurance for heavy tail losses with finite expectations
• Combining traditional and parametric insurance for cost reduction
• Calibrating hybrid contracts to outperform traditional indemnity covers

Innovation

• Combines traditional and parametric insurance methods
• Uses optimization for heavy tail loss calibration
• Employs covariates for instant claim compensation