This paper presents a novel approach to stochastic mortality modelling by using the Conway–Maxwell–Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable choice because it can account for different levels of variability in the data, a feature known as dispersion. Specifically, it can handle data that are underdispersed (less variable than expected), equidispersed (as variable as expected), and overdispersed (more variable than expected). We develop a Bayesian formulation that treats the dispersion level as an unknown parameter, using a Gamma prior to enable a robust and coherent integration of the parameter, process, and distributional uncertainty. The model is calibrated using Markov chain Monte Carlo (MCMC) methods, with model performance evaluated using standard statistical criteria such as residual analysis and scoring rules. An empirical study using England and Wales male mortality data shows that our CMP-based models provide a better fit for both existing data and future predictions compared to traditional Poisson and negative binomial models, particularly when the data exhibit overdispersion. Finally, we conduct a sensitivity analysis with respect to prior specification to assess robustness.

Mortality models that attempt to capture dispersion typically assume a fixed dispersion structure, an assumption that is rarely satisfied in practice and that can lead to miscalibrated uncertainty and poor predictive performance. In this paper, we introduce a flexible framework for explicitly modelling dispersion in mortality data using the Conway–Maxwell–Poisson (CMP) distribution, which accommodates underdispersion, equidispersion, and overdispersion within a unified specification. Rather than imposing a global dispersion parameter, the framework allows both the type and degree of dispersion to vary by age and over time, thus capturing structural heterogeneity that simpler models may overlook. A Bayesian formulation treats dispersion as unknown, with prior structures that coherently propagate parameter, process, and distributional uncertainty. Estimation is carried out via Markov chain Monte Carlo (MCMC) methods. Using empirical death data for males in England and Wales, we show that variability in mortality counts differs substantially across ages and across time periods. This has meaningful implications for the calibration of longevity risk and the pricing of annuity products.

In this paper, we present axiomatic characterizations of certain simple risk-sharing (RS) rules, such as uniform, mean-proportional and covariance-based linear RS rules. These characterizations facilitate a clearer understanding of the principles underlying the application of these rules; they typically include maintaining some degree of anonymity regarding participant data and/or incident-specific data, adopting non-punitive processes and ensuring the equitability and fairness of RS. By formalizing key concepts such as the reshuffling, source-anonymous contributions and strongly aggregate contributions properties, along with their generalizations, we develop a comprehensive framework that clearly expresses these principles and defines the relevant rules. To illustrate, we demonstrate that the uniform RS rule, a simple mechanism in which risks are shared equally, is the only RS rule that satisfies both the reshuffling and source-anonymous contributions properties. This straightforward axiomatic characterization of the uniform RS rule serves as the foundation for exploring similar principles in two broad classes of RS rules, which we call q-proportional RS rules and (q1, q2)-based linear RS rules, respectively. The framework also allows us to introduce specific new RS rules, such as scenario-based RS rules.

In this paper, we explore advanced modifications to the Tweedie regression model in order to address its limitations in modeling aggregate claims for various types of insurance such as automobile, health, and liability. Traditional Tweedie models, while effective in capturing the probability and magnitude of claims, usually fall short in accurately representing the large incidence of zero claims. Our recommended approach involves a refined modeling of the zero-claim process, together with the integration of boosting methods in order to help leverage an iterative process to enhance predictive accuracy. Despite the inherent slowdown in learning algorithms due to this iteration, several efficient implementation techniques that also help precise tuning of parameters like XGBoost, LightGBM, and CatBoost have emerged. Nonetheless, we chose to utilize CatBoost, an efficient boosting approach that effectively handles categorical and other special types of data. The core contribution of our paper is the assembly of separate modeling for zero claims and the application of tree-based boosting ensemble methods within a CatBoost framework, assuming that the inflated probability of zero is a function of the mean parameter. The efficacy of our enhanced Tweedie model is demonstrated through the application of an insurance telematics dataset, which presents the additional complexity of compositional feature variables. Our modeling results reveal a marked improvement in model performance, showcasing its potential to deliver more accurate predictions suitable for insurance claim analytics.

Recent transformative and disruptive advancements in the insurance industry have embraced various InsurTech innovations. In particular, with the rapid progress in data science and computational capabilities, InsurTech is able to integrate a multitude of emerging data sources, shedding light on opportunities to enhance risk classification and claims management. This paper presents a groundbreaking effort as we combine real-life proprietary insurance claims information together with InsurTech data to enhance the loss model, a fundamental component of insurance companies' risk management. Our study further utilizes various machine learning techniques to quantify the predictive improvement of the InsurTech-enhanced loss model over that of the insurance in-house. The quantification process provides a deeper understanding of the value of the InsurTech innovation and advocates potential risk factors that are unexplored in traditional insurance loss modeling. This study represents a successful undertaking of an academic-industry collaboration, suggesting an inspiring path for future partnerships between industry and academic institutions.

While the hurdle Poisson regression is a popular class of models for count data with excessive zeros, the link function in the binary component may be unsuitable for highly imbalanced cases. Ordinary Poisson regression is unable to handle the presence of dispersion. In this paper, we introduce Conway-Maxwell-Poisson (CMP) distribution and integrate use of flexible skewed Weibull link functions as better alternative. We take a fully Bayesian approach to draw inference from the underlying models to better explain skewness and quantify dispersion, with Deviance Information Criteria (DIC) used for model selection. For empirical investigation, we analyze mining injury data for period 2013-2016 from the U.S. Mine Safety and Health Administration (MSHA). The risk factors describing proportions of employee hours spent in each type of mining work are compositional data; the probabilistic principal components analysis (PPCA) is deployed to deal with such covariates. The hurdle CMP regression is additionally adjusted for exposure, measured by the total employee working hours, to make inference on rate of mining injuries; we tested its competitiveness against other models. This can be used as predictive model in the mining workplace to identify features that increase the risk of injuries so that prevention can be implemented.

In this paper, we present axiomatic characterizations of some simple risk-sharing (RS) rules, such as the uniform, the mean-proportional and the covariance-based linear RS rules. These characterizations make it easier to understand the underlying principles when applying these rules. Such principles typically include maintaining some degree of anonymity regarding participants' data and/or incident-specific data, adopting non-punitive processes and ensuring the equitability and fairness of risk sharing. By formalizing key concepts such as the reshuffling property, the source-anonymous contributions property and the strongly aggregate contributions property, along with their generalizations, we develop a comprehensive framework that expresses these principles clearly and defines the relevant rules. To illustrate, we demonstrate that the uniform RS rule, a simple mechanism in which risks are shared equally, is the only RS rule that satisfies both the reshuffling property and the source-anonymous contributions property. This straightforward axiomatic characterization of the uniform RS rule serves as a foundation for exploring similar principles in two broad classes of risk-sharing rules, which we baptize the q-proportional RS rules and the (q_1,q_2)-based linear RS rules, respectively. This framework also allows us to introduce novel particular RS rules, such as the scenario-based RS rules.

Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. Real-world classification problems with severely imbalanced class distributions have increased substantially in recent years. In such cases, significantly fewer observations are available for minority classes to learn from than for majority classes. Despite this sparsity, the minority class is often considered as the more interesting class, yet the development of a scientific learning algorithm that is suitable for these observations presents numerous challenges. In this study, we further explore the merits of an effective multi-class classification algorithm known as SAMME.C2 that is specialized for handling severely imbalanced classes. This innovative method blends the flexible mechanics of the boosting techniques from the SAMME algorithm, which is a multi-class classifier, and the Ada.C2 algorithm, which is a cost-sensitive binary classifier that is designed to address highly imbalanced classes. We establish a scientific and statistical formulation of the SAMME.C2 algorithm, together with providing and explaining the resulting procedure. We demonstrate the consistently superior performance of this algorithm through numerical experiments as well as empirical studies.

Compositional data are multivariate observations that carry only relative information between components. Applying standard multivariate statistical methodology directly to analyze compositional data can lead to paradoxes and misinterpretations. Compositional data also frequently appear in insurance, especially with telematics information. However, such type of data does not receive deserved special treatment in most existing actuarial literature. In this paper, we explore and investigate the use of exponential family principal component analysis (EPCA) to analyze compositional data in insurance. The method is applied to analyze a dataset obtained from the U.S. Mine Safety and Health Administration. The numerical results show that EPCA is able to produce principal components that are significant predictors and improve the prediction accuracy of the regression model. The EPCA method can be a promising useful tool for actuaries to analyze compositional data.

Abstract Background Because of a change of government, the Colombian Ministry of Health and Social Protection is in the process of presenting a structural reform for the General System of Social Security in Health (GSSSH), in order to implement a ‘preventive and predictive health model’. However, it will always be relevant to review and analyze the fiscal implications of any proposed public policy program, to protect financial sustainability and to promote the better functioning of the system in question. Methods To contribute to this topic, we have calculated, using a financial–actuarial approach, the loss ratio for the years 2017 to 2021 for the Capitation Payment Unit (CPU) for all the Health-Promoting Entities (HPE) for both contributory and subsidized schemes. This information, derived from public reports available on the official website of the National Health Superintendency, allows us to estimate the financial burden of the institutions that guarantee access to and provision of health services and technologies in Colombia. Results The study shows that close to half of the HPEs in Colombia (which represent 11.6 million affiliates) have CPU loss ratios of more than 100% for the year 2021, evidencing insufficient resources for the operation of health insurance. Conclusions Finally, we propose some policy recommendations regarding the strengthening of informed decision-making to allow the healthy financial sustainability of the Colombian GSSSH.

Two-part framework and the Tweedie generalized linear model (GLM) have traditionally been used to model loss costs for short-term insurance contracts. For most portfolios of insurance claims, there is typically a large proportion of zero claims that leads to imbalances, resulting in lower prediction accuracy of these traditional approaches. In this article, we propose the use of tree-based methods with a hybrid structure that involves a two-step algorithm as an alternative approach. For example, the first step is the construction of a classification tree to build the probability model for claim frequency. The second step is the application of elastic net regression models at each terminal node from the classification tree to build the distribution models for claim severity. This hybrid structure captures the benefits of tuning hyperparameters at each step of the algorithm; this allows for improved prediction accuracy, and tuning can be performed to meet specific business objectives. An obvious major advantage of this hybrid structure is improved model interpretability. We examine and compare the predictive performance of this hybrid structure relative to the traditional Tweedie GLM using both simulated and real datasets. Our empirical results show that these hybrid tree-based methods produce more accurate and informative predictions.

The health care sector in the United States is complex and is also a large sector that generates about 20% of the country's gross domestic product. Health care analytics has been used by researchers and practitioners to better understand the industry. In this article, we examine and demonstrate the use of Beta regression models to study the utilization of brand name drugs in the United States to understand the variability of brand name drug utilization across different areas. The models are fitted to public datasets obtained from the Medicare & Medicaid Services and the Internal Revenue Service. Integrated nested Laplace approximation (INLA) is used to perform the inference. The numerical results show that Beta regression models can fit the brand name drug claim rates well and including spatial dependence improves the performance of the Beta regression models. Such models can be used to reflect the effect of prescription drug utilization when updating an insured's health risk in a risk scoring model.

plágio, mediante o emprego de ferramentas específicas, e.g.: iThenticate.

Variable annuities have become popular retirement and investment vehicles due to their attractive guarantee features. Nonetheless, managing the financial risks associated with the guarantees poses great challenges for insurance companies. One challenge is risk quantification, which involves frequent valuation of the guarantees. Insurers rely on the use of Monte Carlo simulation as the guarantees are too complicated to be valued by closed-form formulas. Although Monte Carlo simulation is flexible to handle any types of guarantees, it is computationally intensive. Metamodels are increasing in popularity as efficient approaches for addressing the computational issues. In this paper, we empirically explore the use of tree-based models as metamodels for the valuation of the guarantees. In particular, we consider traditional regression trees, tree ensembles, and trees based on unbiased recursive partitioning. We also compare the performance of tree-based models to that of existing models such as ordinary kriging and GB2 regression. Our results show that tree-based models are efficient in producing accurate predictions and the gradient boosting method is considered the most superior.

Death benefits are generally the largest cash flow items that affect the financial statements of life insurers; some may still not have a systematic process to track and monitor death claims. In this article, we explore data clustering to examine and understand how actual death claims differ from what is expected—an early stage of developing a monitoring system crucial for risk management. We extended the k-prototype clustering algorithm to draw inferences from a life insurance dataset using only the insured’s characteristics and policy information without regard to known mortality. This clustering has the feature of efficiently handling categorical, numerical, and spatial attributes. Using gap statistics, the optimal clusters obtained from the algorithm are then used to compare actual to expected death claims experience of the life insurance portfolio. Our empirical data contained observations of approximately 1.14 million policies with a total insured amount of over 650 billion dollars. For this portfolio, the algorithm produced three natural clusters, with each cluster having lower actual to expected death claims but with differing variability. The analytical results provide management a process to identify policyholders’ attributes that dominate significant mortality deviations, and thereby enhance decision making for taking necessary actions.

Powered with telematics technology, insurers can now capture a wide range of data, such as distance traveled, how drivers brake, accelerate or make turns, and travel frequency each day of the week, to better decode driver's behavior. Such additional information helps insurers improve risk assessments for usage-based insurance (UBI), an increasingly popular industry innovation. In this article, we explore how to integrate telematics information to better predict claims frequency. For motor insurance during a policy year, we typically observe a large proportion of drivers with zero claims, a less proportion with exactly one claim, and far lesser with two or more claims. We introduce the use of a cost-sensitive multi-class adaptive boosting (AdaBoost) algorithm, which we call SAMME.C2, to handle such imbalances. To calibrate SAMME.C2 algorithm, we use empirical data collected from a telematics program in Canada and we find improved assessment of driving behavior with telematics relative to traditional risk variables. We demonstrate our algorithm can outperform other models that can handle class imbalances: SAMME, SAMME with SMOTE, RUSBoost, and SMOTEBoost. The sampled data on telematics were observations during 2013-2016 for which 50,301 are used for training and another 21,574 for testing. Broadly speaking, the additional information derived from vehicle telematics helps refine risk classification of drivers of UBI.

This article describes the techniques employed in the production of a synthetic dataset of driver telematics emulated from a similar real insurance dataset. The synthetic dataset generated has 100,000 policies that included observations regarding driver's claims experience, together with associated classical risk variables and telematics-related variables. This work is aimed to produce a resource that can be used to advance models to assess risks for usage-based insurance. It follows a three-stage process while using machine learning algorithms. In the first stage, a synthetic portfolio of the space of feature variables is generated applying an extended SMOTE algorithm. The second stage is simulating values for the number of claims as multiple binary classifications applying feedforward neural networks. The third stage is simulating values for aggregated amount of claims as regression using feedforward neural networks, with number of claims included in the set of feature variables. The resulting dataset is evaluated by comparing the synthetic and real datasets when Poisson and gamma regression models are fitted to the respective data. Other visualization and data summarization produce remarkable similar statistics between the two datasets. We hope that researchers interested in obtaining telematics datasets to calibrate models or learning algorithms will find our work ot be valuable.

In ratemaking, calculation of a pure premium has traditionally been based on modeling frequency and severity in an aggregated claims model. For simplicity, it has been a standard practice to assume the independence of loss frequency and loss severity. In recent years, there is sporadic interest in the actuarial literature exploring models that departs from this independence. In this article, we extend the work of Garrido et al. (2016) which uses generalized linear models (GLMs) that account for dependence between frequency and severity and simultaneously incorporate rating factors to capture policyholder heterogeneity. In addition, we quantify and explain the contribution of the variability of claims among policyholders through the use of random effects using generalized linear mixed models (GLMMs). We calibrated our model using a portfolio of auto insurance contracts from a Singapore insurer where we observed claim counts and amounts from policyholders for a period of six years. We compared our results with the dependent GLM considered by Garrido et al. (2016), Tweedie models, and the case of independence. The dependent GLMM shows statistical evidence of positive dependence between frequency and severity. Using validation procedures, we find that the results demonstrate a more superior model when random effects are considered within a GLMM framework.

Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. There is an increasing growth of real-world classification problems with severely imbalanced class distributions. In this case, minority classes have much fewer observations to learn from than those from majority classes. Despite this sparsity, a minority class is often considered the more interesting class yet developing a scientific learning algorithm suitable for the observations presents countless challenges. In this article, we suggest a novel multi-class classification algorithm specialized to handle severely imbalanced classes based on the method we refer to as SAMME.C2. It blends the flexible mechanics of the boosting techniques from SAMME algorithm, a multi-class classifier, and Ada.C2 algorithm, a cost-sensitive binary classifier designed to address highly class imbalances. Not only do we provide the resulting algorithm but we also establish scientific and statistical formulation of our proposed SAMME.C2 algorithm. Through numerical experiments examining various degrees of classifier difficulty, we demonstrate consistent superior performance of our proposed model.

The insurance industry is one of the most relevant segments for sustainable economic development, not only because it protects society’s assets, but also because it encourages the formation of long-term provisions and reserves. Thus, it is possible to guarantee that advances in income distribution, as well as family consumption, will not regress under adverse scenarios. By promoting virtuous feedback between the productive activity and the legitimate social interest, this sector plays a central role in the promotion of collective well-being. Therefore, Actuarial Science can strongly collaborate in the development of Contemporary Administration.