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.

The classical credibility premium provides a simple and efficient method for predicting future damages and losses. However, when dealing with a nonhomogeneous population, this widely used technique has been challenged by the Regression Tree Credibility (RTC) model and the Logistic Regression Credibility (LRC) model. This article introduces the Mixture Credibility Formula (MCF), which represents a convex combination of the classical credibility premiums of several homogeneous subpopulations derived from the original population. We also compare the performance of the MCF method with the RTC and LRC methods. Our analysis demonstrates that the MCF method consistently outperforms these approaches in terms of the quadratic loss function, highlighting its effectiveness in refining insurance premium calculations and enhancing risk assessment strategies.

We investigate state-level age-specific mortality trends based on the United States Mortality Database (USMDB) published by the Human Mortality Database. In tandem with looking at the longevity experience across all the states, we also consider a collection of socio-demographic, economic, and educational covariates that correlate with mortality trends. To obtain smoothed mortality surfaces for each state, we implement the machine learning framework of Multi-Output Gaussian Process regression (Huynh & Ludkovski, AAS, 2021) on targeted groupings of 3–6 states. Our detailed exploratory analysis shows that the mortality experience is highly inhomogeneous across states in terms of respective Age structures. We moreover document multiple divergent trends between best and worst states, between Females and Males, and between younger and older Ages. The comparisons across the 50+ fitted models offer opportunities for rich insights about drivers of mortality in the U.S. and are visualized through numerous figures and an online interactive dashboard.

We seek to understand the factors that drive mortality in the contiguous United States using data that are indexed by county and year and grouped into 18 different age bins. We propose a model that adds two important contributions to existing mortality studies. First, we treat age as a random effect. This is an improvement over previous models because it allows the model in one age group to borrow information from other age groups. Second, we utilize Gaussian Processes to create nonlinear covariate effects for predictors such as unemployment rate, race, and education level. This allows for a more flexible relationship to be modeled between mortality and these predictors. Understanding that the United States is expansive and diverse, we allow for many of these effects to vary by location. The flexibility in how predictors relate to mortality has not been used in previous mortality studies and will result in a more accurate model and a more complete understanding of the factors that drive mortality. Both the multivariate nature of the model as well as the spatially varying non-linear predictors will advance the study of mortality and will allow us to better examine the relationships between the predictors and mortality.

The rise of large language models (LLMs) has marked a substantial leap toward artificial general intelligence. However, the utilization of LLMs in (re)insurance sector remains a challenging problem because of the gap between general capabilities and domain-specific requirements. Two prevalent methods for domain specialization of LLMs involve prompt engineering and fine-tuning. In this study, we aim to evaluate the efficacy of LLMs, enhanced with prompt engineering and fine-tuning techniques, on quantitative reasoning tasks within the (re)insurance domain. It is found that (1) compared to prompt engineering, fine-tuning with task-specific calculation dataset provides a remarkable leap in performance, even exceeding the performance of larger pre-trained LLMs; (2) when acquired task-specific calculation data are limited, supplementing LLMs with domain-specific knowledge dataset is an effective alternative; and (3) enhanced reasoning capabilities should be the primary focus for LLMs when tackling quantitative tasks, surpassing mere computational skills. Moreover, the fine-tuned models demonstrate a consistent aptitude for common-sense reasoning and factual knowledge, as evidenced by their performance on public benchmarks. Overall, this study demonstrates the potential of LLMs to be utilized as powerful tools to serve as AI assistants and solve quantitative reasoning tasks in (re)insurance sector.

Tree-based methods are widely used in insurance pricing due to their simple and accurate splitting rules. However, there is no guarantee that the resulting premiums avoid indirect discrimination when features recorded in the database are correlated with the protected variable under consideration. This paper shows that splitting rules in regression trees and random forests can be adapted in order to avoid indirect discrimination related to a binary protected variable like gender. The new procedure is illustrated on motor third-party liability insurance claim data.

Disaster Risk Financing (DRF) presents a massive challenge to governments worldwide in protecting against catastrophic disaster losses. This study explores the development of a Disaster Fund that optimally integrates various DRF instruments, considering several real-world factors, including limited reserves, constrained risk horizons, risk aversion, risk tolerance, insurance structures, and premium pricing strategies. We demonstrate that the Value-at-Risk (VaR) and Tail VaR constraints are equivalent when the government has a limited risk horizon. Furthermore, we investigate the optimality of various insurance structures under different premium principles, conduct comparative statics on key parameters, and analyze the influence of a VaR constraint on the optimal mix of disaster financing instruments. Lastly, we apply our Disaster Fund model to the National Flood Insurance Program dataset to assess the optimal disaster financing strategy within the context of our framework.

Accurate mortality forecasting is crucial for actuarial pricing, reserving, and capital planning, yet the traditional Lee-Carter model struggles with non-linear age and cohort patterns, coherent multi-population forecasting, and quantifying prediction uncertainties. Recent advances in deep learning provide a range of tools that can address these limitations, but actuarial surveys have not kept pace. This paper provides the first concise view of deep learning in mortality forecasting. We cover six deep network architectures, namely Recurrent Neural Networks, Convolutional Neural Networks, Transformers, Autoencoders, Locally Connected Networks, and Multi-Task Feed-Forward Networks. We discuss how these architectures tackle cohort effects, population coherence, interpretability, and uncertainty in mortality forecasting. Evidence from the literature shows that carefully calibrated deep learning models can consistently outperform the Lee-Carter baselines; however, no single architecture resolves every challenge, and open issues remain with data scarcity, interpretability, uncertainty quantification, and keeping pace with the advances of deep learning. This review is also intended to provide actuaries with a practical roadmap for adopting deep learning models in mortality forecasting.

This paper examines an insurer’s optimal asset allocation and reinsurance policies. The financial market framework includes one risk-free and one risky asset. The insurer has two business lines, where the ordinary claim process is modeled by a compound Poisson process and catastrophic claims follow a compound dynamic contagion process. The dynamic contagion process, which is a generalization of the externally exciting Cox process with shot-noise intensity and the self-exciting Hawkes process, is enhanced by accommodating the dependency structure between the magnitude of contribution to intensity after initial events for catastrophic insurance products and its claim/loss size. We also consider the dependency structure between the positive effect on the intensity and the negative crashes on the risky financial asset when initial events occur. Our objective is to maximize the insurer’s expected utility of terminal surplus. We construct the extended Hamilton–Jacobi–Bellman (HJB) equation using dynamic programming principles to derive an explicit optimal reinsurance policy for ordinary claims. We further develop an iterative scheme for solving the value function and the optimal asset allocation policy and the reinsurance policy for catastrophic claims numerically, providing a rigorous convergence proof. Finally, we present numerical examples to demonstrate the impact of key parameters.

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.