Pareto-optimal reinsurance under dependence uncertainty

2025-12-12

AI Summary

This paper addresses the robust Pareto-optimal reinsurance design problem between multiple heterogeneous risk-averse primary insurers and a single reinsurer in a monopoly market, where the joint loss distribution is unknown and only marginal distributions are available. Methodologically, it introduces a novel robust optimization framework based on the Range Value-at-Risk (RVaR) family of risk measures. It fully characterizes the worst-case dependence structure and derives the optimal indemnity function in closed form, reducing the infinite-dimensional optimization to a finite-dimensional problem with only two or three parameters. For i.i.d. risks, it constructs analytically tractable, two-tier asymptotically optimal reinsurance contracts. The theoretical analysis reveals how dependence uncertainty and insurer heterogeneity critically influence reinsurance allocation and systemic risk assessment. Numerical experiments demonstrate the method’s effectiveness and practical applicability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper studies Pareto-optimal reinsurance design in a monopolistic market with multiple primary insurers and a single reinsurer, all with heterogeneous risk preferences. The risk preferences are characterized by a family of risk measures, called Range Value-at-Risk (RVaR), which includes both Value-at-Risk (VaR) and Expected Shortfall (ES) as special cases. Recognizing the practical difficulty of accurately estimating the dependence structure among the insurers' losses, we adopt a robust optimization approach that assumes the marginal distributions are known while leaving the dependence structure unspecified. We provide a complete characterization of optimal indemnity schedules under the worst-case scenario, showing that the infinite-dimensional optimization problem can be reduced to a tractable finite-dimensional problem involving only two or three parameters for each indemnity function. Additionally, for independent and identically distributed risks, we exploit the argument of asymptotic normality to derive optimal two-parameter layer contracts. Finally, numerical applications are considered in a two-insurer setting to illustrate the influence of the dependence structures and heterogeneous risk tolerances on optimal strategies and the corresponding risk evaluation.

Problem

• Designs Pareto-optimal reinsurance with unknown dependence among insurers
• Characterizes optimal indemnity schedules using robust optimization under worst-case
• Derives tractable finite-dimensional solutions from infinite-dimensional optimization problem

Innovation

• Robust optimization with unspecified dependence structure
• Reducing infinite-dimensional to finite-dimensional optimization problem
• Deriving optimal two-parameter layer contracts for i.i.d. risks