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)
Munich Re surpasses profit guidance for a fifth consecutive year, achieving every target of its Ambition 2025 strategy programme - munichre.com
In the 2025 financial year, Munich Re posted a net result of €6,121m (5,690m) – surpassing the original target of €6bn. And 2025 was the fifth consecutive year in which our annual profit outperformed the respective guidance.
Read source → • munichre.comWorkers’ Comp:Quiet Overachiever in P/C Insurance
Read source → • Triple-I🔬 Research Spotlight (arXiv)
Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting
arXiv • Score: 27 • 2026-02-18
We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.
Open paper →From Chain-Ladder to Individual Claims Reserving
arXiv • Score: 26 • 2026-02-17
The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure. Instead of rolling forward the cumulative claims with estimated CL factors, we estimate multi-period factors that project the latest observations directly to the ultimate claims. This alternative perspective on CL reserving creates a natural pathway for the application of machine learning techniques to individual claims reserving. As a proof of concept, we present a small-scale real data application employing neural networks for individual claims reserving.
Open paper →Hidden multistate models to study multimorbidity trajectories
arXiv • Score: 18 • 2026-02-20
Multimorbidity in older adults is common, heterogeneous, and highly dynamic, and it is strongly associated with disability and increased healthcare utilization. However, existing approaches to studying multimorbidity trajectories are largely descriptive or rely on discrete-time models, which struggle to handle irregular observation intervals and right-censoring. We developed a continuous-time hidden multistate modeling framework to capture transitions among latent multimorbidity patterns while accounting for interval censoring and misclassification. A simulation study compared alternative model specifications under varying sample sizes and follow-up schemes, and the best-performing specification was applied to longitudinal data from the Swedish National study on Aging and Care-Kungsholmen (SNAC-K), including 2,716 multimorbid participants followed for up to 18 years. Simulation results showed that hidden multistate models substantially reduced bias in transition hazard estimates compared to non-hidden models, with fully time-inhomogeneous models outperforming piecewise approximations. Application to SNAC-K confirmed the feasibility and practical utility of this framework, enabling identification of risk factors for accelerated progression toward complex multimorbidity and revealing a gradient of mortality risk across patterns. Continuous-time hidden multistate models provide a robust alternative to traditional approaches, supporting individualized predictions and informing targeted interventions and secondary prevention strategies for multimorbidity in aging populations.
Open paper →Competing Risk Analysis in Cardiovascular Outcome Trials: A Simulation Comparison of Cox and Fine-Gray Models
arXiv • Score: 16 • 2026-02-17
Cardiovascular outcome trials commonly face competing risks when non-CV death prevents observation of major adverse cardiovascular events (MACE). While Cox proportional hazards models treat competing events as independent censoring, Fine-Gray subdistribution hazard models explicitly handle competing risks, targeting different estimands. This simulation study using bivariate copula models systematically varies competing event rates (0.5%-5% annually), treatment effects on competing events (50% reduction to 50% increase), and correlation structures to compare these approaches. At competing event rates typical of CV outcome trials (~1% annually), Cox and Fine-Gray produce nearly identical hazard ratio estimates regardless of correlation strength or treatment effect direction. Substantial divergence occurs only with high competing rates and directionally discordant treatment effects, though neither estimator provides unbiased estimates of true marginal hazard ratios under these conditions. In typical CV trial settings with low competing event rates, Cox models remain appropriate for primary analysis due to superior interpretability. Pre-specified Cox models should not be abandoned for competing risk methods. Importantly, Fine-Gray models do not constitute proper sensitivity analyses to Cox models per ICH E9(R1), as they target different estimands rather than testing assumptions. As supplementary analysis, cumulative incidence using Aalen-Johansen estimator can provide transparency about competing risk impact. Under high competing-risk scenarios, alternative approaches such as inverse probability of censoring weighting, multiple imputation, or inclusion of all-cause mortality in primary endpoints warrant consideration.
Open paper →Until next time—stay credible.
— The Credibility Report
Edition 009 | Prepared March 1, 2026 (UTC)