When Indemnity Insurance Fails: Parametric Coverage under Binding Budget and Risk Constraints

Paper: arXiv 2512.21973

Authors: Benjamin Avanzi, Debbie Kusch Falden, Mogens Steffensen

Abstract

In high-risk environments, traditional indemnity insurance is often unaffordable or ineffective, despite its well-known optimality under expected utility. We compare excess-of-loss indemnity insurance with parametric insurance within a common mean-variance framework, allowing for fixed costs, heterogeneous premium loadings, and binding budget constraints. Motivated by the disaster insurance and risk-sharing literature, we show that, once these realistic frictions are introduced, parametric insurance can yield higher welfare for risk-averse individuals, even under the same utility objective and without relying on behavioral assumptions. The welfare advantage arises precisely when indemnity insurance becomes impractical, and disappears once both contracts are unconstrained. Our results help reconcile classical insurance theory with the growing use of parametric risk transfer in high-risk settings.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous closed-form theoretical analysis of parametric versus excess-of-loss indemnity insurance under budget and risk constraints using a Poisson-exponential compound loss framework. While it is strong analytically and highly clear in its motivation and positioning within classical insurance theory, it is primarily a mathematical microeconomic paper with limited empirical validation or real-world backtesting data.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Indemnity vs. Parametric Insurance under Realistic Constraints] --> B[Inputs: Mean-Variance Utility, Budget Constraints, Fixed Costs, Loading Factors]
    B --> C[Formulate Optimization Models for Indemnity & Parametric Contracts]
    C --> D[Compare Welfare Outcomes Under Binding Budget Constraints]
    D --> E[Outcome: Parametric Insurance Yields Higher Welfare in High-Risk/Constrained Settings]
    D --> F[Outcome: Advantage Disappears When Budget Constraints Are Removed]