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)
Fire and Allied Lines: Recent Success in a Challenging Market
Read source → • Triple-IResilient Post-Wildfire Rebuilding Pays Off
Read source → • Triple-IRead More about: Nat Cat sigma 1/2026
Read source → • Swiss Re InstituteRead More about: sigma 5/2025: Shifting sands: global economic and insurance market outlook
Read source → • Swiss Re InstituteRead More about: sigma 04/2025: Life (span) insurance: accumulation, decumulation and longevity solutions
Read source → • Swiss Re InstituteRead More about: sigma 03/2025: Growing stronger: Property & Casualty market adapts to riskier world
Read source → • Swiss Re Institute🔬 Research Spotlight (arXiv)
Optimal Insurance Menu Design under the Expected-Value Premium Principle
arXiv • Score: 37 • 2026-04-17
This paper studies optimal insurance design under asymmetric information in a Stackelberg framework, where a monopolistic insurer faces uncertainty about both the insured's risk attitude, captured by a risk-aversion parameter, and the insured's risk type, characterized by the loss distribution. In particular, when the risk type is unobservable, we allow the risk-aversion parameter to depend on the risk type. We construct a menu of contracts that maximizes the mean-variance utilities of both parties under the expected-value premium principle, subject to a truth-telling constraint that ensures the truthful revelation of private information. We show that when risk attitude is private information, the optimal coverage takes the form of excess-of-loss insurance with linear pricing in terms of the risk loading (defined as the premium minus the expected loss), designed to screen risk preferences. In contrast, when risk type is unobserved, we restrict the coverage function to an excess-of-loss form and derive an ordinary differential equation that characterizes the optimal risk loading. Under mild conditions, we establish the existence and uniqueness of the solution. The results show that equilibrium contracts exhibit nonlinear pricing with decreasing risk loadings, implying that higher-risk individuals face lower risk loadings in order to induce self-selection. Finally, numerical illustrations demonstrate how parameter values and the distributions of unobserved heterogeneity affect the structure of optimal contracts and the resulting pricing schedule.
Open paper →Revealing Geography-Driven Signals in Zone-Level Claim Frequency Models: An Empirical Study using Environmental and Visual Predictors
arXiv • Score: 34 • 2026-04-23
Geographic context is often consider relevant to motor insurance risk, yet public actuarial datasets provide limited location identifiers, constraining how this information can be incorporated and evaluated in claim-frequency models. This study examines how geographic information from alternative data sources can be incorporated into actuarial models for Motor Third Party Liability (MTPL) claim prediction under such constraints. Using the BeMTPL97 dataset, we adopt a zone-level modeling framework and evaluate predictive performance on unseen postcodes. Geographic information is introduced through two channels: environmental indicators from OpenStreetMap and CORINE Land Cover, and orthoimagery released by the Belgian National Geographic Institute for academic use. We evaluate the predictive contribution of coordinates, environmental features, and image embeddings across three baseline models: generalized linear models (GLMs), regularized GLMs, and gradient-boosted trees, while raw imagery is modeled using convolutional neural networks. Our results show that augmenting actuarial variables with constructed geographic information improves accuracy. Across experiments, both linear and tree-based models benefit most from combining coordinates with environmental features extracted at 5 km scale, while smaller neighborhoods also improve baseline specifications. Generally, image embeddings do not improve performance when environmental features are available; however, when such features are absent, pretrained vision-transformer embeddings enhance accuracy and stability for regularized GLMs. Our results show that the predictive value of geographic information in zone-level MTPL frequency models depends less on model complexity than on how geography is represented, and illustrate that geographic context can be incorporated despite limited individual-level spatial information.
Open paper →Optimal basis risk weighting in expectile-based parametric insurance
arXiv • Score: 20 • 2026-04-23
Parametric insurance contracts translate index measurements to compensation for policyholders' losses using predefined payment schemes. These need to be designed carefully to keep basis risk, i.e. the disparity between payouts and true damages, small. Previous research has motivated the use of conditional expectiles as payment schemes, whose compensation is impacted by the policyholder's potentially unknown attitude towards basis risk. To alleviate this model uncertainty and to investigate the impact of (hidden) influencing factors, we characterize existence and uniqueness of the optimal basis risk weighting in a utility-maximization framework through a set of boundary conditions. In the absence of an optimal solution, we provide comparisons to the utility of no insurance and full indemnity coverage. We establish a link between location-scale distributions and separability of conditional expectiles' derivatives, thus improving the understanding of these statistical functionals. A simulation study on parametric hurricane insurance visualizes our results, investigates the influence of premium loading and risk aversion on the optimal weighting, and comments on the challenge of (spatial) loss dependence.
Open paper →On the market-consistent valuation of health insurance liabilities
arXiv • Score: 16 • 2026-04-20
Up to inflation, the basic cash flow associated to health insurance policies is independent from capital markets. It has therefore been common to calculate the Best Estimate based on a deterministic approach. However, in the light of volatile inflation dynamics in recent years, it has become more popular to use stochastic models for the Best Estimate of health insurance policies. In this article, we show that this stochastic approach is preferable and provide a framework to efficiently evaluate a large stock of health insurance policies. More precisely, we first prove that the Best Estimate of a life-long health insurance policy depends on the choice of model for the interest and inflation rates. That is, the Best Estimate is not uniquely determined by the current nominal and real spot rates used to calibrate these type of models -- even without profit participation or the common practice of limiting premium adjustments. Second, we construct a valuation portfolio for life-long health insurance policies without the common industry practice of limiting the premium adjustments, decomposing the Best Estimate into 1.) deterministic coefficients derived from policy data and 2.) the prices of basis financial instruments that are independent of the individual policy data. Using this decomposition, the policies do not have to be tracked individually along each generated inflation path. This allows a very efficient evaluation of the Best Estimate for a large stock of policies with a stochastic model.
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 017 | Prepared April 26, 2026 (UTC)