Paper: arXiv 2512.11430

Authors: Tim J. Boonen, Xia Han, Peng Liu, Jiacong Wang

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation of Pareto-optimal reinsurance using Range Value-at-Risk (RVaR) under robust optimization and dependence uncertainty. While the mathematical proofs and dimension reduction theorems are sophisticated and highly novel, the empirical rigor is limited to numerical illustrations with simulated data rather than empirical market backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Design Pareto-optimal reinsurance under dependence uncertainty with RVaR risk measures"] --> B["Inputs: Insurers' marginal loss distributions & RVaR parameters (heterogeneous preferences)"]
    B --> C["Methodology: Robust optimization under worst-case dependence scenario"]
    C --> D["Computational Process: Dimension reduction from infinite-dimensional problem to finite-dimensional parameters"]
    D --> E["Special Case Analysis: Asymptotic normality applied to i.i.d. risks for optimal 2-parameter layer contracts"]
    E --> F["Outcomes: Tractable optimal indemnity schedules & numerical insights on risk tolerance impact"]