Paper: arXiv 2504.17468

Authors: Ka Chun Cheung, Sheung Chi Phillip Yam, Fei Lung Yuen, Yiying Zhang

Abstract

In this article, we employ a principal-agent model to analyze optimal contract design in a monopolistic reinsurance market under adverse selection with a continuum of insurer types. Instead of using the classical expected utility framework, we model each insurer’s risk preference through their VaR at their chosen risk tolerance level. Under informational asymmetry, the reinsurer (principal) seeks to maximize expected profit by offering an optimal menu of reinsurance contracts to a continuum of insurers (agents) with hidden characteristics. To avoid the complexity of the traditional duality approach, which yields indirect multivariate utility functions, we introduce a change of variables that reduces the problem to a univariate one. We show that the optimal indirect utility for both stop-loss and quota-share reinsurance is in stop-loss form, implying that the reinsurer will classify agents into two risk groups-high and low-even in the continuum setting. Utilizing this new class of indirect utility functions, we fully solve the problem for three common reinsurance structures: stop-loss, quota-share, and change-loss. Numerical examples are also provided for illustrating the main findings.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly rigorous mathematical analysis of contract design under adverse selection with VaR risk measures and a continuum of agent types. While it introduces an innovative change-of-variables technique to solve a complex optimization problem, it is entirely theoretical with minimal empirical validation beyond illustrative numerical examples.

Research Flowchart

  flowchart TD
    A[Goal: Optimal Reinsurance Contract Design under Adverse Selection & VaR Risk Preferences] --> B[Input: Principal-Agent Model with a Continuum of Insurer Types & Hidden Characteristics]
    B --> C[Methodology: Introduce Change of Variables to Reduce Multivariate Duality to Univariate Problem]
    C --> D[Computational Analysis: Solve Incentive Compatibility for Stop-Loss, Quota-Share, & Change-Loss Structures]
    D --> E[Key Outcome: Optimal Indirect Utility Takes a Stop-Loss Form]
    E --> F[Main Finding: Reinsurer Segregates Continuum of Insurers into Two Discrete Groups: High & Low Risk]

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0 of 75 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.