Paper: arXiv 2501.05672

Authors: Zongxia Liang, Zhaojie Ren, Bin Zou

Abstract

This paper studies an optimal reinsurance problem for a utility-maximizing insurer, subject to the reinsurer’s endogenous default and background risk. An endogenous default occurs when the insurer’s contractual indemnity exceeds the reinsurer’s available reserve, which is random due to the background risk. We obtain an analytical solution to the optimal contract for two types of reinsurance contracts, differentiated by whether their indemnity functions depend on the reinsurer’s background risk. The results shed light on the joint effect of the reinsurer’s default and background risk on the insurer’s reinsurance demand.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation of optimal reinsurance under endogenous default and background risk, deriving analytical analytical multi-layer and deductible contract solutions. However, it is purely theoretical and mathematical with no empirical data analysis or backtesting presented in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Reinsurance with Endogenous Default & Background Risk] --> B[Inputs: Insurer Utility, Background Risk, Reinsurer Reserve]
    B --> C[Methodology: Utility Maximization Modeling]
    C --> D[Analyze Indemnity Functions: Dependent vs. Independent of Background Risk]
    D --> E[Derive Analytical Solutions for Optimal Contracts]
    E --> F[Findings: Characterized Joint Effect of Default & Background Risk on Demand]

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and 50 more
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1 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.