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)
Lloyd’s market delivers solid first half performance, despite softening rate environment and rising geopolitical tensions - Lloyd's insurance
Lloyd’s, the only insurance marketplace of its kind in the world, today announced its results for the first six months of 2026, reporting gross written premium of £34.7bn (HY 2025: £32.5bn) and a combined ratio of 90.8% (HY 2025: 92.5%).
Read source → • Lloyd's insuranceRead More about: World Insurance
Read source → • Swiss Re InstituteRead More about: sigma 2/2025: World insurance in 2025: a riskier, more fragmented world order
Read source → • Swiss Re InstituteRead More about: sigma 1/2025: Natural catastrophes: insured losses on trend to USD 145 billion in 2025
Read source → • Swiss Re Institute🔬 Research Spotlight (arXiv)
Scaling Laws, Tabular Data and Actuarial Ratemaking Models
arXiv • Score: 32 • 2026-09-02
Scaling laws in modern deep learning describe how held-out loss improves as model capacity, training data, and compute increase, often following power-law trends. We investigate whether analogous scaling regularities arise in actuarial ratemaking, where data are tabular, heterogeneous, and noisy, and where classical models such as GLMs remain strong baselines. Using a real-world motor insurance portfolio, we train models from different families across increasing fractions of the training data and multiple random seeds, evaluating out-of-sample Poisson deviance, a likelihood-based loss for Poisson count predictions in which lower values indicate better held-out fit. We find that all model families improve with additional data, but scaling exponents differ substantially: TabM exhibits markedly stronger data scaling than purely supervised tabular Transformers and standard MLP baselines. Transformer variants show weak parameter scaling unless augmented with additional inductive biases (TabM-style adaptation or self-supervision). These results provide quantitative guidance on model selection by data regime and suggest that effective scaling on actuarial tabular tasks depends on architecture and loss function objective design, with simple increases in Transformer size providing limited gains.
Open paper →Adaptive singular-point method for pricing and hedging surrenderable equity-linked contracts
arXiv • Score: 26 • 2026-09-01
We propose a deterministic numerical method for pricing and hedging surrenderable equity-linked life-insurance contracts with periodic premiums and fund contributions, maturity and death guarantees, and Bermudan surrender under correlated stochastic volatility and stochastic interest rates. The main computational challenge is the non-recombining accumulated fund, which couples with multiple stochastic factors and early exercise. Our key idea is to avoid a full multidimensional fund lattice: variance and interest-rate factors are discretized on recombining lattices, while at each factor node the contract value is represented as an adaptive one-dimensional function of the fund. Periodic contributions then act as translations of the fund argument, whereas surrender is handled directly through a backward obstacle condition. Piecewise-cubic representations propagate payoff and exercise singularities and are compressed by continuous pruning criteria that control the representation error. We establish weak convergence of the financial chains, convergence of the adaptive valuation under vanishing representation error, and Delta consistency on regular fund regions. For the strict binomial scheme, additional regularity yields first-order weak accuracy and a Talay-Tubaro expansion supporting Richardson extrapolation. Numerical experiments show compact representations, favorable cost--accuracy, and close agreement with independent Monte Carlo and cross-fitted least-squares Monte Carlo benchmarks. Hedging results further show that contracts with similar values can generate materially different exposures to equity, volatility, and interest-rate risk.
Open paper →Text Data Analysis and Classification Methods - Insights from Customer Letters in Life Insurance
arXiv • Score: 23 • 2026-08-30
The business of life insurance companies is characterized by long-term contracts. For this reason, data describing customers is of immense value. A portion of the data provided to the customer is rarely or not at all analyzed. This includes customer letters of any kind. This work focuses on classifying customer letters as cancellations and identifying the respective reason, if available. The outlined approach can also be applied to other business transactions and reasons. We discuss data acquisition and preparation, present alternatives, and explain the reasons for the chosen approach. A successful implementation of such a tool can lead to a better understanding of customer cancellation behavior by the insurer, enabling more targeted actions in certain situations.
Open paper →Neural Networks Learning the Radon--Nikodym Derivative: Empirical Option Pricing in Incomplete Markets
arXiv • Score: 22 • 2026-09-01
In incomplete markets, no-arbitrage (NFLVR) guarantees the existence, not the uniqueness, of an equivalent local martingale measure (ELMM): unhedgeable risks (jumps, stochastic volatility) admit a whole family of equivalent measures, and asset dynamics alone cannot pin down the one the market selects. We characterize the identifiability of $Q$ from option data and propose a measure that is identifiable from data yet prices any claim consistently. The key boundary is an ``identification wall'': European options identify only the terminal marginal, while out-of-sample tails and path/joint structure require instruments matched to the priced risk (variance or higher-moment swaps, path-dependent claims). Within this view, minimum-relative-entropy weighted Monte Carlo (WMC) is the optimal baseline for the marginal; we generalize it to a full path-space measure change parameterized by a neural network on physical scenarios---XiNet---which learns $ξ=\mathrm{d}\mathbb{Q}/\mathrm{d}\mathbb{P}$ directly from 8 model-free path features, with option prices as a soft constraint. On European (marginal) pricing XiNet matches but does not surpass WMC, and both are bound by the identification wall out-of-sample. On path-dependent claims the picture reverses: calibrated on the same European surface, per-marginal methods fail structurally (an ATM forward-start is mispriced by $\sim+100\%$), whereas XiNet's single self-consistent measure keeps the bias to $+0.3\%$, beating maximum-entropy WMC ($-24\%$), because $ξ=f_θ(\text{path features})$ captures joint structure Europeans cannot constrain. Identification is thus risk-specific, and XiNet is a single measure that absorbs available instruments and prices all claims consistently.
Open paper →On the approximation of posterior laws in compound loss models by conditional Wasserstein GANs
arXiv • Score: 15 • 2026-08-27
Bayesian inference in compound loss models must often be repeated across policies, market scenarios, and prior specifications. Outside conjugate cases, this may require repeated numerical integration or Markov chain Monte Carlo (MCMC). We formulate this problem as amortized posterior approximation and construct a conditional Wasserstein generative adversarial network conditioned on sufficient statistics, prior mean and coefficient of variation, and mixture weights of prior families. Notably, a single shared generator is able to approximate the posterior laws of both the Poisson intensity and the Pareto shape parameter under mixtures of Gamma, inverse-Gaussian, and lognormal priors. We assess the approximation by simulation-based calibration and by comparisons with analytical posteriors, deterministic quadrature, and extensive MCMC simulations. In an application to data on extreme natural catastrophe losses, we produce rolling one-year posterior predictive distributions, and examine the effects of heavy-tailed severity and prior-family uncertainty on aggregate tail risk.
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 036 | Prepared September 6, 2026 (UTC)