Abstract This paper assesses the impact of demographic risk on a portfolio of equity-linked insurance contracts featuring a Cliquet-style guarantee, in which the policyholder accrues, on an annual basis, interest equal to the maximum between the return on a risky portfolio and a guaranteed minimum rate. We provide closed-form expressions for inflows, outflows, and reserves for such a portfolio through a cohort-based approach. In accordance with market-consistent actuarial principles, we determine both the no-arbitrage value of the liabilities and the structure of the hedging portfolio that replicates the guaranteed benefits. We quantify demographic risk by separately assessing the capital requirements for both idiosyncratic and trend risks. The capital requirement is computed over a one-year horizon using a 99.5% Value-at-Risk measure, consistent with the Solvency II regulatory framework. The model accommodates different regulatory contexts, allowing for jurisdiction-specific rules and accounting standards. Numerical simulations highlight how the portfolio’s risk profile is affected by demographic volatility, which is influenced by policyholder age, policy duration, and dispersion of the sums insured. Additionally, trend risk depends on both mortality volatility and the specification of the longevity model. This framework supports insurers in evaluating, hedging, and managing demographic risk in market-linked life insurance products.

Abstract The Nelson–Siegel model is widely used in fixed income markets to produce yield curve dynamics. The multiple time-dependent parameter model conveniently addresses the level, slope, and curvature dynamics of the yield curves. In this study, we present a novel state-space functional regression model that incorporates a dynamic Nelson–Siegel (DNS) model and functional regression formulations applied to a multi-economy setting. This framework offers distinct advantages in explaining the relative spreads in yields between a reference economy and a response economy. To address the inherent challenges of model calibration, a kernel principal component analysis is employed to transform the representation of functional regression into a finite-dimensional, tractable estimation problem. A comprehensive empirical analysis is conducted to assess the efficacy of the functional regression approach, including an in-sample performance comparison with the DNS model. We conducted the stress testing analysis of the yield curves’ term structure within a dual economy framework. The bond ladder portfolio was examined through a case study focused on spread modeling using historical data for US Treasury and UK bonds.

Abstract The InsurTech industry has undergone almost a decade of development. Despite its initial success, the industry now faces challenges from global uncertainties and regulatory adjustments, which lead to concerns about sustainable profit growth and the ongoing development of InsurTech. This study provides an overview of the evolution of InsurTech development from both academic and practical perspectives. A bibliometric analysis of more than 20,000 published articles, including both practice articles and academic articles, is put forward. As compared to other review articles in this field, which often focus on either the practice or the scholarly side of development, this article brings together a review of both academic and practice-based articles from fields relevant to InsurTech including artificial intelligence, the Internet of Things, and also powerful computing technology. A keyword extraction framework is developed and applied. Using text analysis, this study reviews the prioritized topics, analyzes the robustness of the development of publication growth, identifies emerging insurance business lines, and also highlights the challenges and gaps in both academic and practice development. This study aims to motivate collaboration between academics and industry to face the challenges posed by the integration of InsurTech into insurance operations.

Abstract We evaluate the performance and level of intergenerational cross-subsidy in flat-accrual and dynamic-accrual collective defined contribution (CDC) schemes, which have been designed to be compatible with UK legislation. In the flat-accrual scheme, all members accrue the benefits at the same rate, irrespective of age. This captures the most significant feature of the Royal Mail Collective Pension Plan, which is currently the only UK CDC scheme. The dynamic-accrual schemes seek to reduce intergenerational cross-subsidies by varying the rate of benefit-accrual schemes in accordance with the age of members and the current funding level. We find that these CDC schemes can often be successful in smoothing pension outcomes postretirement while outperforming a defined contribution scheme followed by annuity purchase at the point of retirement. However, this out-performance is not guaranteed in a flat-accrual scheme, and there is little smoothing of projected pension outcomes before retirement. There are significant intergenerational cross-subsidies in the flat-accrual scheme, which qualitatively mirror the cross-subsidies seen in defined benefit schemes, but the magnitude of cross-subsidies is much larger in flat-accrual CDC schemes. The dynamic-accrual scheme design seeks to reduce such cross-subsidies, but we find significant cross-subsidies still arise due to the approximate pricing methodology used to determine the benefits.

Abstract Gaussian Process (GP) modeling is a probabilistic, non-parametric framework for describing spatio-temporal dependence that is well-suited for fitting risk-related surfaces. I summarize the main emerging actuarial use cases of GPs, including their applications in longevity modeling, insurance contract valuation, and loss development. The editorial also discusses further contexts with potential for GP-based approaches.

Abstract This paper addresses the gap between theoretical modeling of cyber risk propagation and empirical analysis of loss characteristics by introducing a novel approach that integrates both approaches. We model the development of cyber loss counts over time using a discrete-time susceptible-infected-recovered process, linking these counts to covariates, and modeling loss severity with regression models. By incorporating temporal and covariate-dependent transition rates, we eliminate the scaling effect of population size on infection counts, revealing the true underlying dynamics. Simulations show that this susceptible-infected-recovered framework significantly improves aggregate loss prediction accuracy, providing a more effective and practical tool for actuarial assessments and risk management in the cyber risk context.

Abstract We employ an appropriate change of measure technique to offer a general result connecting a general form of the Gerber–Shiu function with the distribution of the deficit at ruin under the new (exponentially tilted) measure. Exploiting this result, we extract closed-form formulae for special forms of the Gerber–Shiu function assuming two cases of bivariate distributions that describe the dependence structure between claim sizes and inter-claim times. More specifically, initially, we employ the Downton–Moran bivariate exponential distribution, and we offer explicit formulae for cases of the Gerber–Shiu functions that include the time and the number of claims until ruin. In addition, we derive a closed formula for the defective discounted joint density of the number of claims until ruin, the deficit at ruin, and the time until ruin. The same is achieved for the joint density of the number of claims and the deficit at ruin. We further generalize these results by assuming that the inter-claim times and the claim sizes follow a Kibble–Moran bivariate Erlang distribution. Finally, we offer numerical examples in order to illustrate our main results.

Abstract Credibility theory provides a fundamental framework in actuarial science for estimating policyholder premiums by blending individual claims experience with overall portfolio data. Bühlmann and Bühlmann–Straub credibility models are widely used because, in the Bayesian hierarchical setting, they are the best linear Bayes estimators, minimizing the Bayes risk (expected squared error loss) within the class of linear estimators given the experience data for a particular risk class. To improve estimation accuracy, quadratic credibility models incorporate higher-order terms, capturing more information about the underlying risk structure. This study develops a robust quadratic credibility (RQC) framework that integrates second-order polynomial adjustments of robustly transformed ground-up loss data, such as winsorized moments, to improve stability in the presence of extreme claims or heavy-tailed distributions. Extending semi-linear credibility, RQC maintains interpretability while enhancing statistical efficiency. We establish its asymptotic properties, derive closed-form expressions for the RQC premium, and demonstrate its superior performance in reducing mean square error (MSE). We additionally derive semi-linear credibility structural parameters using winsorized data, further strengthening the robustness of credibility estimation. Analytical comparisons and empirical applications highlight RQC’s ability to capture claim heterogeneity, offering a more reliable and equitable approach to premium estimation. This research advances credibility theory by introducing a refined methodology that balances efficiency, robustness, and practical applicability across diverse insurance settings.

Abstract Fine-grained mortality forecasting has gained momentum in actuarial research due to its ability to capture localized, short-term fluctuations in death rates. This paper introduces MortFCNet , a deep-learning method that predicts weekly death rates using region-specific weather inputs. Unlike traditional Serfling-based methods and gradient-boosting models that rely on predefined fixed Fourier terms and manual feature engineering, MortFCNet automatically learns patterns from raw time-series data without needing explicitly defined Fourier terms or manual feature engineering. Extensive experiments across over 200 NUTS-3 regions in France, Italy, and Switzerland demonstrate that MortFCNet consistently outperforms both a standard Serfling-type baseline and XGBoost in terms of predictive accuracy. Our ablation studies further confirm its ability to uncover complex relationships in the data without feature engineering. Moreover, this work underscores a new perspective on exploring deep learning for advancing fine-grained mortality forecasting.

Abstract The practice of actuarial science has always been rooted in computation. From the early days of hand-constructed tables and commutation functions to today’s large-scale stochastic simulations and machine learning models, actuaries have continuously adapted their analytical tools to the technology of their time. The rapid growth of high-performance computing, open-source software, and data-driven methodologies now offers new possibilities for actuarial modeling – transforming not only how we calculate, but also how we think about risk, uncertainty, and decision-making. This editorial introduces a thematic collection on Actuarial Software, which showcases recent advances at the intersection of actuarial modeling and computational science.