Paper: arXiv 2402.11580

Authors: Zongxia Liang, Xiaodong Luo

Abstract

We study a reinsurance Stackelberg game in which both the insurer and the reinsurer adopt the mean-variance (abbr. MV) criterion in their decision-making and the reinsurance is irreversible. We apply a unified singular control framework where irreversible reinsurance contracts can be signed in both discrete and continuous times. The results theoretically illustrate that, rather than continuous-time contracts or a bunch of discrete-time contracts, a single once-for-all reinsurance contract is preferred. Moreover, the Stackelberg game turns out to be centering on the signing time of the single contract. The insurer signs the contract if the premium rate is lower than a time-dependent threshold and the reinsurer designs a premium that triggers the signing of the contract at his preferred time. Further, we find that reinsurance preference, discount and reversion have a decreasing dominance in the reinsurer’s decision-making, which is not seen for the insurer.

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 provides a strong theoretical contribution using a unified singular control framework to solve a Stackelberg reinsurance game with irreversibility and mean-variance criteria. However, it is entirely theoretical with no empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Question: Optimal MV Reinsurance Decisions<br/>under Irreversibility & Stackelberg Game"] --> B["Inputs: Insurer/Reinsurer Risk Profiles,<br/>Premium Rates, Discount & Reversion Parameters"]
    B --> C["Methodology: Singular Control Framework<br/>for Discrete & Continuous Contract Signing"]
    C --> D["Computational Process: Solve MV Optimization<br/>to Find Trigger Thresholds & Optimal Signing Time"]
    D --> E["Key Findings: Single 'Once-for-All' Contract Preferred"]
    E --> F["Outcomes: Reinsurer Controls Timing via Premium;<br/>Reinsurance Preference Dominates Reinsurer's Decisions"]