The Credibility Report
Actuarial Intelligence for Insurance Professionals
What’s in this edition
Primary-source market updates (no aggregator links) plus the latest actuarial-relevant arXiv papers (score ≥ 15, last 14 days).
📰 Headlines (primary sources)
Protection gap means minimal insured losses after Philippines earthquake - S&P Global
Read source → • S&P Global🔬 Research Spotlight (arXiv)
Pricing Excess-of-Loss Reinsurance and CAT Bonds under Climate Uncertainty: A Cox Process Framework with Temperature-Dependent Stochastic Intensity
arXiv • Score: 47 • 2026-06-12
This paper develops a climate-aware pricing framework for excess-of-loss (XL) reinsurance contracts and catastrophe (CAT) bonds under non-stationary catastrophe risk. Catastrophe arrivals are modeled as a Cox process whose stochastic intensity depends exponentially on a temperature-related climate index. To represent climate dynamics, the index is modeled as a mean-reverting Ornstein--Uhlenbeck process around a time-dependent warming trend. Within this setting, aggregate losses follow a compound Cox structure with lognormal severities. Pricing is performed under a reduced-form risk-adjusted measure, which provides a tractable valuation approach for XL reinsurance layers and binary zero-coupon CAT bond payoffs in an incomplete market setting. Because catastrophe losses are not dynamically replicable, the framework emphasizes scenario-based valuation rather than model-independent no-arbitrage bounds. A Monte Carlo valuation scheme is implemented to quantify the economic implications of climate-dependent catastrophe intensity. The numerical results show that climate dependence materially changes the loss-generation mechanism and affects the valuation of catastrophe-linked contracts. In the baseline calibration, the climate-aware model increases the excess-of-loss reinsurance premium and lowers the CAT bond price relative to the stationary benchmark. Furthermore, our analysis of the 99.5\% Tail Value-at-Risk (TVaR) indicates that stationary benchmarks may underestimate economic capital requirements by approximately 13.7\% compared to the climate-aware framework, highlighting the potential regulatory relevance of the proposed model. This finding highlights that benchmark design is critical for interpreting climate-pricing effects.
Open paper →Gaming-Resistant Insurance Contracts for Autonomous AI Agents: Strategy-Proof Toll Mechanism Design
arXiv • Score: 19 • 2026-06-15
Paper A defines a time-consistent actuarial runtime that prices each side-effect-bearing action against a contractually fixed safe default and gates execution against a reserve budget. It treats the operator as passive. This paper makes the operator strategic. We characterise a five-attack space for autonomous AI-agent insurance contracts and prove when the actuarial runtime is gaming-resistant. Two attack surfaces -- post-toll safe-default selection and within-boundary action splitting -- are closed by Paper A's minimal-authority and no-splitting clauses. The remaining three require new contract clauses. First, common-control aggregation prevents cross-boundary re-routing from reducing toll below the boundary potential applied to total exposure. Second, interface failures such as invalid JSON are contract-relevant events, not safety wins: treating them as zero-toll safe defaults can reward unreliable models, while escalation fees reverse the incentive. We validate this interface-compliance theorem on committed cross-model traces from the companion empirical paper. Third, a model-identity menu with a componentwise-minimum penalty schedule makes truthful reporting of the deployed model weakly dominant. We then compose these clauses with Paper A's runtime guarantees to obtain joint incentive compatibility over the five-attack space. Finally, a two-parameter premium family discharges operator individual rationality and weak budget balance at the truthful equilibrium. The result is an incentive-compatibility layer for actuarial control of autonomous-agent side effects.
Open paper →Gradient boosting for extremes: sampling theory and application to insurance
arXiv • Score: 18 • 2026-06-12
We develop a statistical learning theory for gradient boosting applied to the estimation of covariate-dependent Generalized Pareto (GP) distributions in the context of Peaks-over-Threshold modeling. After an orthogonal reparametrization of the GP likelihood that diagonalizes its Fisher information matrix, we cast the estimation problem within the Empirical Risk Minimization (ERM) framework and derive non-asymptotic error bounds for the boosting estimator. Our analysis accounts for three distinct sources of error in the process: statistical fluctuations, the approximation bias inherent to the asymptotic nature of the GP model-controlled under second-order regular variation-and the approximation error associated with the finite number of boosting iterates, making explicit the resulting bias-variance trade-off. We illustrate the practical benefits of the reparametrization through simulations, showing that it significantly reduces gradient correlation during training and improves convergence stability. The methodology is applied to a medical malpractice insurance dataset from the Texas Department of Insurance, comprising over 18 000 closed claims. The gradient boosting approach yields a good fit for the tail of settlement cost distributions and reveals that the number of days to settlement is the dominant predictor of tail heaviness, consistent with earlier findings in the reserving literature.
Open paper →✅ Practical Takeaways
- For P&C pricing and capital work, refresh wildfire and severe-convective-storm accumulation scenarios rather than relying on last year’s peril mix.
- For property underwriting, test whether post-wildfire resilient rebuilding standards justify explicit mitigation credits or revised rebuild-cost assumptions.
- For MTPL frequency models, benchmark zone-level coordinates and environmental features against the existing tariff variables before adding more complex image embeddings.
- For health insurance valuation, run stochastic inflation and interest-rate sensitivity alongside deterministic best-estimate calculations.
Until next time—stay credible.
— The Credibility Report
Edition 025 | Prepared June 21, 2026 (UTC)