Arbitrage-free catastrophe reinsurance valuation for compound dynamic contagion claims

Paper: arXiv 2502.13325

Authors: Jiwook Jang, Patrick J. Laub, Tak Kuen Siu, Hongbiao Zhao

Abstract

In this paper, we consider catastrophe stop-loss reinsurance valuation for a reinsurance company with dynamic contagion claims. To deal with conventional and emerging catastrophic events, we propose the use of a compound dynamic contagion process for the catastrophic component of the liability. Under the premise that there is an absence of arbitrage opportunity in the market, we obtain arbitrage-free premiums for these contracts. To this end, the Esscher transform is adopted to specify an equivalent martingale probability measure. We show that reinsurers have various ways of levying the security loading on the net premiums to quantify the catastrophic liability in light of the growing challenges posed by emerging risks arising from climate change, cyberattacks, and pandemics. We numerically compare arbitrage-free catastrophe stop-loss reinsurance premiums via the Monte Carlo simulation method. We also compare them with those from generalised compound Hawkes/compound Cox cases. Sensitivity analyses are performed by changing the retention level, the Esscher parameters and the intensity parameters.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework applying a compound dynamic contagion process and the Esscher transform to value catastrophe reinsurance contracts. However, the empirical component relies on synthetic Monte Carlo simulations and sensitivity analysis rather than backtesting against historical market claims data.

Research Flowchart

  flowchart TD
    A[Research Goal: Valuation of Catastrophe Stop-Loss Reinsurance under Dynamic Contagion Risks] --> B[Model Formulation: Compound Dynamic Contagion Process for Catastrophic Claims]
    B --> C[Pricing Framework: Apply Esscher Transform for Arbitrage-Free Equivalent Martingale Measure]
    C --> D[Inputs: Retention Level, Esscher Parameters, Intensity Parameters & Risk Drivers]
    D --> E[Computation: Monte Carlo Simulations & Benchmark Comparisons with Hawkes/Cox Models]
    E --> F[Key Outcomes: Derived Arbitrage-Free Premiums, Security Loading Methods & Sensitivity Analyses]