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Copyright of Scientia Iranica. Transaction E, Industrial Engineering is the property of Scientia Iranica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Developing an informed lapse management strategy (LMS) is critical for life insurers to improve profitability and gain insight into the risk of their global portfolio. Prior research in actuarial science has shown that targeting policyholders by maximising their individual customer lifetime value is more advantageous than targeting all those likely to lapse. However, most existing lapse analyses do not leverage the variability of features and targets over time. We propose a longitudinal LMS framework, utilising tree-based models for longitudinal data, such as left-truncated and right-censored (LTRC) trees and forests, as well as mixed-effect tree-based models. Our methodology provides time-informed insights, leading to increased precision in targeting. Our findings indicate that the use of longitudinally structured data significantly enhances the precision of models in predicting lapse behaviour, estimating customer lifetime value, and evaluating individual retention gains. The implementation of mixed-effect random forests enables the production of time-varying predictions that are highly relevant for decision-making. This paper contributes to the field of lapse analysis for life insurers by demonstrating the importance of exploiting the complete past trajectory of policyholders, which is often available in insurers' information systems but has yet to be fully utilised. [ABSTRACT FROM AUTHOR]

In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings and many of their special cases. We provide necessary and/or sufficient conditions for the orderings by comparing the underlying model parameters. In addition, we investigate the (positive) linear forms of usual stochastic, convex and increasing convex, positive convex and increasing-positive-convex orderings. Using these theoretical results, we explore two applications. The first involves determining the upper bound of multivariate skew-elliptical risk variables under specific parameter constraints. The other one focuses on assessing the portfolio aggregation risks. Finally, two examples based on numerical simulations and real data from an Australian insurance company illustrate the established results and practical explanations. [ABSTRACT FROM AUTHOR]

AbstractIn the context of actuarial science, the second largest claim amount is crucial to insurance analysis since they provide useful information for determining annual premium. In this article, we provide sufficient conditions of the second largest claim amounts arising from two sets of dependent and heterogeneous individual risk models according to various stochastic orders. It is first shown that the reversed hazard order between the occurrence probabilities vectors implies the reversed hazard order of the second largest claim amounts under certain conditions. Second, sufficient conditions are established for the usual stochastic ordering of the second largest claim amounts arising from heterogeneous dependent individual risk models under copula dependence. Finally, several examples illustrating the theoretical results are presented as well. [ABSTRACT FROM AUTHOR]

This article proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector Z, independent of X and Y, the scale parameter of this class of distributions is mixed with a function α (Z) and its skew parameter is mixed with another function β (Z). Sufficient (and necessary) conditions are established for stochastically comparing different random vectors stemming from this class of distributions by means of several stochastic orders including the usual stochastic order, convex order, increasing convex order, supermodular order, and some related linear orders. Two insightful assumptions for the density generators of elliptical distributions, aiming to control the generators' tail, are provided to make stochastic comparisons among mixed-elliptical vectors. Some applications in applied probability and actuarial science are also provided as illustrations on the main findings. [ABSTRACT FROM AUTHOR]

Claims with high severity and low probability constitute a high risk for the insurance market. One tool to deal with this kind of event is the Extreme Value Theory (EVT). The main goal of this article is to apply the EVT to Actuarial Science using a different estimator for parameters, allowing the calculation of pure reinsurance premiums and the choice for the retention limit for insurance companies. The execution was split into two parts: (i) comparing the estimators through simulations, and; (ii) using data from 5 SUSEP lines of business with different natures, intending to estimate some extreme value statistics. In simulation studies, the Pickands estimator was very promising, but the limited amount of data resulted in a great variance when applied to real cases. Lastly, we concluded that the EVT is a powerful tool for insurance, capturing the behavior of extreme clams amount better than traditional models. [ABSTRACT FROM AUTHOR]

The traditional modeling of dependence among branches in non-life insurance has historically rested on the assumption of independence between risks. However, recent studies have brought to light that overlooking the interdependence between risks is not prudent. An illustrative example is found in automobile insurance, where a discernible connection exists between the number of claims in the Automobile Damage branch and those in the Automobile Civil Liability branch. This paper aims to delve into the utilization of copula functions for modeling the interrelationships among claims charges across diverse branches within a non-life insurance portfolio. Moreover, it seeks to assess the consequential impacts of these dependencies on the capital requirements of AXA Insurance in the Moroccan market. Our research concentrates on four pivotal branches within AXA Insurance, namely "work accidents", "automobile civil liability", "disability", and "fire, marine, aviation, and transport". Through a thorough analysis encompassing dependency measurements, independence tests, and various graphical representations, we have substantiated the existence of interdependencies among the claim costs associated with these four risk branches. Importantly, our findings underscore that assuming independence leads to a slight underestimation of the capital requirement needed for effective risk accumulation management by the insurer. [ABSTRACT FROM AUTHOR]

Calling attention to the growing intersection between the insurance and technology sectors—or 'insurtech'—this article is intended as a bat signal for the interdisciplinary fields that have spent recent decades studying the explosion of digitization, datafication, smartification, automation, and so on. Many of the dynamics that attract people to researching technology are exemplified, often in exaggerated ways, by emerging applications in insurance, an industry that has broad material effects. Based on in-depth mixed-methods research into insurance technology, I have identified a set of interlocking logics that underly this regime of actuarial governance in society: ubiquitous intermediation, continuous interaction, total integration, hyper-personalization, actuarial discrimination, and dynamic reaction. Together these logics describe how enduring ambitions and existing capabilities are motivating the future of how insurers engage with customers, data, time, and value. This article surveys each logic, laying out a techno-political framework for how to orient critical analysis of developments in insurtech and where to direct future research on this growing industry. Ultimately, my goal is to advance our understanding how insurance—a powerful institution that is fundamental to the operations of modern society—continues to change, and what dynamics and imperatives, whose desires and interests are steering that change. The stuff of insurance is far too important to be left to the insurance industry. [ABSTRACT FROM AUTHOR]

It is becoming increasingly evident that educators need to prioritize the welfare of their students, particularly those who are underperforming academically, also known as "students at risk". By analyzing learning behaviors, including attendance records, past academic results, and online interactions, we can identify students at risk and provide them with timely support. Therefore, this study aimed to develop a prediction model for identifying students at risk in an actuarial science course and suggest an intervention strategy. Our study was comprised of five components of learning analytics: data collection, reporting, prediction, intervention, and reassessment. Prior to applying a prediction model, correlation analysis was utilized to identify variables impacting students' academic performance. Three variables, including CGPA, pre-requisite subject marks, and assessment marks were considered due to their rather strong correlation with the final marks of the course. Then, quadratic discriminant analysis (QDA) was applied to predict students classified as "at risk" and "not as risk". Out of 69 students from the course, 15 students identified as "at risk" and 40 students participated in the Peer Assisted Learning Program (PALP) as an intervention strategy to reduce the course's failure rate. We cannot conclude whether PALP was an effective intervention strategy for students at risk because a majority of them failed to attend. However, we observed that those who attended PALP had a higher likelihood of passing the course. Our prediction model had high rates of accuracy, precision, sensitivity, and specificity, which were 91%, 98%, 91%, and 91%, respectively. Therefore, QDA could be considered a robust model for predicting students at risk. We have outlined some limitations and future studies at the end of our study. [ABSTRACT FROM AUTHOR]

The study of mortality is an ever-active field of research, and new methods or combinations of methods are constantly being developed. In the actuarial domain, the study of phenomena disrupting mortality and leading to excess mortality, as in the case of COVID-19, is of great interest. Therefore, it is relevant to investigate the extent to which an epidemiological model can be integrated into an actuarial approach in the context of mortality. The aim of this project is to establish a method for the study of excess mortality due to an epidemic and to quantify these effects in the context of the insurance world to anticipate certain possible financial instabilities. We consider a case study caused by SARS-CoV-2 in Belgium during the year 2020. We propose an approach that develops an epidemiological model simulating excess mortality, and we incorporate this model into a classical approach to pricing life insurance products. [ABSTRACT FROM AUTHOR]

The article discusses the intersection of genetic testing and actuarial science in the context of life insurance. It highlights the complexities of genetic information, emphasizing that genetic variation is not limited to single-gene disorders like Huntington's disease. The article explores the potential for adverse selection in insurance and the need for actuaries to rely on medical studies to make underwriting decisions. It also examines the regulatory responses to genetic information in different countries. The author concludes that while genetic testing has not yet fully integrated into mainstream medicine, there is still a role for actuaries in understanding and navigating the implications of genetic information in insurance. [Extracted from the article]

The Pareto distribution is of paramount importance in actuarial science, wealth distribution, finance, etc. This paper introduces a control chart inspired by Shewhart's methodology, designed for monitoring shifts in the Pareto distribution through a repetitive sampling approach. The chart employs a modified statistic that combines shape and threshold parameters as its plotting statistic. Coefficients for the Shewhart-type Pareto chart are computed for two-phase limits. The performance of the suggested chart is assessed in terms of run length characteristics, assuming a shift in the process mean. Additionally, we conduct an efficiency comparison with existing control charts. The findings suggest that, on average, the proposed Pareto chart demonstrates greater efficiency in promptly detecting changes compared to alternative methods. To illustrate the practical application of our approach, we present an example using revenue data. [ABSTRACT FROM AUTHOR]

Copulas are quite a popular, flexible, and useful tool for multivariate modeling in many fields of applications, including finance and insurance, actuarial sciences, biomedical studies, geostatistics, and hydrology. In this paper, we use the concept of diagonal function to build new bivariate copulas based on the well known and important Ali–Mikhail–Haq (AMH), Farlie–Gumbel–Morgenstern (FGM) and Plackett families. We also study some dependence properties of the newly constructed semilinear copulas, namely, the Spearman's ρ coefficient. In particular, we find that the range of this rank correlation coefficient varies between weak and moderate values for the transformed AMH and FGM families, although it varies between moderate and strong values for the transformed Plackett families. Moreover, in all cases, the Spearman's ρ coefficient reaches negative and positive values. Finally, we present a synthetic data generation algorithm, as well as a classical method of estimation of the copula association parameter for each of the six transformed bivariate families. [ABSTRACT FROM AUTHOR]

This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann's alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form [ G (·) ] λ , where λ > 0 and G (·) is a continuous cumulative distribution function. This mixture can be useful in economics, financial, and actuarial fields, where extreme and long tails appear in the empirical data. The special case in which G (·) is the Stoppa cumulative distribution function, which is a good description of the random behaviour of large losses, is studied in detail. We provide properties of this mixture, mainly related to the analysis of the tail of the distribution that makes it a candidate for fitting actuarial data with extreme observations. Inference procedures are discussed and applications to three well-known datasets are shown. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Hubei Open Vocational College is the property of Journal of Hubei Open Vocational College Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Suppose X1, ..., Xn are scale proportional hazards random variables, and I p 1 , ... , I p n are independent Bernoulli random variables, independent of the Xi's, i = 1, ..., n. Let Y i = I p i X i , for i = 1, ..., n. In actuarial science, Yi corresponds to the claim amount in a portfolio of risks. In this paper, we establish usual stochastic order between the largest claim amounts when the matrix of parameters changes to another matrix in a certain mathematical sense. Under certain conditions, by using the concept of vector majorization, we also discuss stochastic comparisons between the smallest claim amounts in the sense of the usual stochastic order with dependent claim severities. We then apply the results for some special cases of the scale proportional hazards model with possibly different proportional hazards and scale parameters to illustrate the established results. [ABSTRACT FROM AUTHOR]

But to achieve these objectives, actuaries and actuarial science have to work with climate scientists, as they are the leading experts to provide detailed information on historical weather patterns, ongoing climate changes, and future climate predictions. This includes developing new insurance or financial products for climate-related risks, for example flood and crop insurance, and pricing these risks appropriately, or improving product design to incentivize risk mitigation. While there is a growing interest in climate-related risks within the actuarial profession, professionals and climate scientists sometimes lack the resources to help them quantify the financial impacts of climate change. [Extracted from the article]

Modelling claim frequency and claim severity are topics of great interest in property-casualty insurance for supporting underwriting, ratemaking, and reserving actuarial decisions. Standard Generalized Linear Models (GLM) frequency–severity models assume a linear relationship between a function of the response variable and the predictors, independence between the claim frequency and severity, and assign full credibility to the data. To overcome some of these restrictions, this paper investigates the predictive performance of Gradient Boosting with decision trees as base learners to model the claim frequency and the claim severity distributions of an auto insurance big dataset and compare it with that obtained using a standard GLM model. The out-of-sample performance measure results show that the predictive performance of the Gradient Boosting Model (GBM) is superior to the standard GLM model in the Poisson claim frequency model. Differently, in the claim severity model, the classical GLM outperformed the Gradient Boosting Model. The findings suggest that gradient boost models can capture the non-linear relation between the response variable and feature variables and their complex interactions and thus are a valuable tool for the insurer in feature engineering and the development of a data-driven approach to risk management and insurance. [ABSTRACT FROM AUTHOR]

Previous work has highlighted the need to apply stochastic modeling to understand the dynamics of phenomena occurring in the insurance industry. In this paper, for life insurance and applying a stochastic approach under efficient markets, we use survival probabilities and stochastic differential equations to model the actuarial reserve, changes in the constituted actuarial reserve, and estimated income over time. We present an application, sensitivity analysis, and discussion of the results using United States life tables.

The study of mortality is an ever-active field of research, and new methods or combinations of methods are constantly being developed. In the actuarial domain, the study of phenomena disrupting mortality and leading to excess mortality, as in the case of COVID-19, is of great interest. Therefore, it is relevant to investigate the extent to which an epidemiological model can be integrated into an actuarial approach in the context of mortality. The aim of this project is to establish a method for the study of excess mortality due to an epidemic and to quantify these effects in the context of the insurance world to anticipate certain possible financial instabilities. We consider a case study caused by SARS-CoV-2 in Belgium during the year 2020. We propose an approach that develops an epidemiological model simulating excess mortality, and we incorporate this model into a classical approach to pricing life insurance products.

An analysis was performed on millions of quotes by a number of insurance companies, covering a major part of the automobile insurance market in Spain. As expected, it was observed that the range of prices can be partially explained by the variables directly associated with the risk being insured in each case (vehicle specifications, age, driver experience, etc.), although there are considerable differences in some cases that are not explained by the said variables and that have a strong dependency on the geographical location of the risk. By using context data from open sources associated with the different Spanish provinces (vehicle fleet, climate, socio-economic data, among others), the premium estimation models are complemented and the price differences are better explained. The use of this type of data and models can help insurance companies to adapt their premium rating and identify possible market opportunities. [ABSTRACT FROM AUTHOR]

Machine learning, a subfield of artificial intelligence, emphasizes the creation of algorithms capable of learning from data and generating predictions. However, in actuarial science, the interpretability of these models often presents challenges, raising concerns about their accuracy and reliability. Explainable artificial intelligence (XAI) has emerged to address these issues by facilitating the development of accurate and comprehensible models. This paper conducts a comparative analysis of various XAI approaches for tackling distinct data-driven insurance problems. The machine learning methods are evaluated based on their accuracy, employing the mean absolute error for regression problems and the accuracy metric for classification problems. Moreover, the interpretability of these methods is assessed through quantitative and qualitative measures of the explanations offered by each explainability technique. The findings reveal that the performance of different XAI methods varies depending on the particular insurance problem at hand. Our research underscores the significance of considering accuracy and interpretability when selecting a machine-learning approach for resolving data-driven insurance challenges. By developing accurate and comprehensible models, we can enhance the transparency and trustworthiness of the predictions generated by these models. [ABSTRACT FROM AUTHOR]

This paper aims to introduce novel systemic risk indicators based on risk allocation methods employed in actuarial science. We present diverse general approaches for constructing these indicators and utilize them to derive indicators based on commonly used risk measures such as Value at Risk, Tail Value at Risk, and Expectiles. Furthermore, we analyze the influence of the dependence structure on the behavior of these indicators using a range of copula models. To support our findings, we provide numerical illustrations. [ABSTRACT FROM AUTHOR]

Risk measurement and insurance pricing have always been issues of concern in actuarial science. Under the framework of uncertainty theory, this paper puts forward a new premium principle: uncertain standard deviation premium principle, proposes some of its properties about risk and compares the premiums of different risks. Based on the utility function of risk aversion, the additional premium coefficient is derived and two specific numerical examples are used to calculate the maximum premium. Furthermore, the unknown parameters of the policy with deductible are estimated by uncertain moment estimation and uncertain maximum likelihood estimation. [ABSTRACT FROM AUTHOR]

Quantiles are a fundamental concept in extreme value theory. They can be obtained from a minimization framework using an asymmetric absolute error loss criterion. The companion notion of expectiles, based on asymmetric squared rather than asymmetric absolute error loss minimization, has received substantial attention from the fields of actuarial science, finance, and econometrics over the last decade. Quantiles and expectiles can be embedded in a common framework of Lp‐quantiles, whose extreme value properties have been explored very recently. Although this generalized notion of quantiles has shown potential for the estimation of extreme quantiles and expectiles, available estimators remain quite difficult to use: they suffer from substantial bias, and the question of the choice of the tuning parameter p remains open. In this article, we work in a context of heavy tails and construct composite bias‐reduced estimators of extreme quantiles and expectiles based on Lp‐quantiles. We provide a discussion of the data‐driven choice of p and of the anchor Lp‐quantile level in practice. The proposed methodology is compared with existing approaches on simulated data and real data. [ABSTRACT FROM AUTHOR]

The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series expression by convolution. We compare both methods, as well as a new normalized saddlepoint approximation, and normal and single distribution negative binomial approximations. We show that the exact series expression used lots of memory when the number of random variables was high (>7). The normalized saddlepoint approximation gives an output with a high relative error (around 3–5%), which can be a problem in some situations. The convolution method is a good compromise for applied practitioners, considering the amount of memory used, the computing time, and the precision of the estimates. However, a simplistic implementation of the algorithm could produce incorrect results due to the non-monotony of the convergence rate. The tolerance limit must be chosen depending on the expected magnitude order of the estimate, for which we used the answer generated by the saddlepoint approximation. Finally, the normal and negative binomial approximations should not be used, as they produced outputs with a very low accuracy. [ABSTRACT FROM AUTHOR]

Abstract The Capitation Payment Unit (CPU) financing mechanism constitutes more than 70% of health spending in Colombia, with a budget allocation of close to 60 trillion Colombian pesos for the year 2022 (approximately 15.7 billion US dollars). This article estimates actuarially, using modern techniques, the CPU for the contributory regime of the General System of Social Security in Health in Colombia, and compares it with what is estimated by the Ministry of Health and Social Protection. Using freely available information systems, by means of statistical copulas functions and artificial neural networks, pure risk premiums are calculated between 2015 and 2021. The study concludes that the weights by risk category are systematically different, showing historical pure premiums surpluses in the group of 0–1 years and deficits (for the regions normal and cities) in the groups over 54 years of age.

Tweedie models can be used to analyze nonnegative continuous data with a probability mass at zero. There have been wide applications in natural science, healthcare research, actuarial science, and other fields. The performance of existing Tweedie models can be limited on today's complex data problems with challenging characteristics such as nonlinear effects, high-order interactions, high-dimensionality and sparsity. In this article, we propose a kernel Tweedie model, Ktweedie, and its sparse variant, SKtweedie, that can simultaneously address the above challenges. Specifically, nonlinear effects and high-order interactions can be flexibly represented through a wide range of kernel functions, which is fully learned from the data; In addition, while the Ktweedie can handle high-dimensional data, the SKtweedie with integrated variable selection can further improve the interpretability. We perform extensive simulation studies to justify the prediction and variable selection accuracy of our method, and demonstrate the applications in ratemaking and loss-reserving in general insurance. Overall, the Ktweedie and SKtweedie outperform existing Tweedie models when there exist nonlinear effects and high-order interactions, particularly when the dimensionality is high relative to the sample size. The model is implemented in an efficient and user-friendly R package ktweedie (). [ABSTRACT FROM AUTHOR]

Background: Establishing the risk of malignant transformation (MT) in oral leukoplakia is usually based on grading oral epithelial dysplasia (OED) on biopsy tissue, for which two systems are proposed: a 3‐tier and a binary system. Only very few actuarial studies have tested the accuracy of such methods in predicting MT, especially for the binary system. This study aimed to assess the accuracy of the two grading systems in predicting MT in a cohort of oral leukoplakia (OL) from Brazil, with follow‐up data. Methods: The sample comprised 878 individuals diagnosed with OL from 2005 to 2018. Follow‐up data were obtained both locally and from the regional cancer registry. All lesions were graded using both the 3‐tier and the binary systems. Kaplan–Meier curves (Log‐rank Mantel‐Cox) were used to assess risk and kappa to assess interobserver agreement. Results: Thirty‐five individuals underwent MT (4%). Both systems demonstrated prognostic value, though the 3‐tier system proved superior, with OR 9.23 (3.42–23.69), PPV 0.152, NPV 0.98, compared to binary OR 3.49 (1.79–6.79), PPV 0.079, NPV 0.976. Interobserver agreement was also superior in the 3‐tier system (0.47, p < 0.05) compared to the binary system (0.139, p = 0.39). Combining the two systems enhanced prognostic values (OR 14.28, PPV 0.217, NPV 0.981). Conclusion: The 3‐tier system presented superior prognostic value to the binary system. Combining both systems to double‐grade intermediate lesions might enhance risk assessment. [ABSTRACT FROM AUTHOR]

Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values <1 correspond to life histories with an increasing mortality rate with age (i.e. actuarial senescence), whereas values >1 correspond to species with a decreasing mortality rate with age (negative senescence), and a Keyfitz entropy of exactly 1 corresponds to a constant mortality rate with age. Keyfitz' entropy was originally defined using a continuous‐time model, and has since been discretised to facilitate its calculation from discrete‐time demographic data.Here, we show that the previously used discretisation of the continuous‐time metric does not preserve the relationship with increasing, decreasing or constant mortality rates. To resolve this discrepancy, we propose a new discrete‐time formula for Keyfitz' entropy for age‐classified life histories.We show that this new method of discretisation preserves the relationship with increasing, decreasing, or constant mortality rates. We analyse the relationship between the original and the new discretisation, and we find that the existing metric tends to underestimate Keyfitz' entropy for both short‐lived species and long‐lived species, thereby introducing a consistent bias.To conclude, to avoid biases when classifying life histories as (non‐)senescent, we suggest researchers use either the new metric proposed here, or one of the many previously suggested survivorship shape metrics applicable to discrete‐time demographic data such as Gini coefficient or Hayley's median. [ABSTRACT FROM AUTHOR]

This research study proposes the inclusion of randomness or an error term in the modified Lee–Carter model, which improves the traditional Lee–Carter model for modeling and forecasting mortality risk for years in the actuarial science field. While the modified Lee–Carter model points out some of its common shortcomings , it has no distributional assumption that has been placed on the error/disturbance term. Incorporating a Gaussian distributional assumption on the error term is proposed, and then, the deep learning technique is used to obtain the parameter estimates. It is a departure from the traditional singular value decomposition estimation technique for estimating the parameters in the model. Finally, the Bühlmann credibility approach is incorporated into the model to determine its forecasting precision compared to the classical Lee–Carter model before applied in actuarial valuations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables. [ABSTRACT FROM AUTHOR]

Regression models in which the response variable has a compound distribution have applications in actuarial science. For example, the aggregate claim amount in a vehicle insurance portfolio can be modeled using a compound Poisson distribution. In this paper, we propose a regression model, wherein the response variable is assumed to have a compound Conway–Maxwell–Poisson (CMP) distribution. This distribution is a parsimonious two-parameter Poisson distribution that accounts for both over- and under-dispersed count data, making it more suitable for application in various fields. A two-part methodology in the framework of a generalized linear model is proposed to estimate the parameters. Additionally, a method to obtain the prediction interval of the response variable is developed. The workings of the proposed methodology are illustrated through simulated data. An application of the compound CMP regression model to real-life vehicle insurance claims data is presented. [ABSTRACT FROM AUTHOR]

Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address a decision maker's (DM's) risk preference. This paper aims to fill out the gap. Specifically, we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk preference is ambiguous. We introduce a preference robust distortion risk measure (PRDRM), which is based on the worst‐case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well‐known general principles such as concavity and inverse S‐shapedness of distortion functions (overweighting on events from impossible to possible or possible to certainty and underweighting on those from possible to more possible) as well as new user‐specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelope of a set of points to characterize the curvature of the distortion function and derive a tractable reformulation of the PRDRM when the underlying random loss is discretely distributed. Moreover, we show that the worst‐case distortion function is a nondecreasing piecewise linear function and can be determined by solving a linear programming problem. Finally, we apply the proposed PRDRM to a risk capital allocation problem and carry out some numerical tests to examine the efficiency of the PRDRM model. [ABSTRACT FROM AUTHOR]

Under-dispersed count data often appear in clinical trials, medical studies, demography, actuarial science, ecology, biology, industry and engineering. Although the generalized Poisson (GP) distribution possesses the twin properties of under- and over-dispersion, in the past 50 years, many authors only treat the GP distribution as an alternative to the negative binomial distribution for modeling over-dispersed count data. To our best knowledge, the issues of calculating maximum likelihood estimates (MLEs) of parameters in GP model without covariates and with covariates for the case of under-dispersion were not solved up to now. In this paper, we first develop a new minimization–maximization (MM) algorithm to calculate the MLEs of parameters in the GP distribution with under-dispersion, and then we develop another new MM algorithm to compute the MLEs of the vector of regression coefficients for the GP mean regression model for the case of under-dispersion. Three hypothesis tests (i.e., the likelihood ratio, Wald and score tests) are provided. Some simulations are conducted. The Bangladesh demographic and health surveys dataset is analyzed to illustrate the proposed methods and comparisons with the existing Conway–Maxwell–Poisson regression model are also presented. [ABSTRACT FROM AUTHOR]

Statistical methods are essential for describing, predicting, and modeling natural phenomena in numerous application areas. These methods are helpful for modeling and predicting data in medicine, reliability engineering, actuarial science, and other fields. This paper presents a novel, simple, and fully flexible modified gamma model. The new model provides various forms of densities, including symmetric, asymmetric, unimodal, and reversed-J shapes, as well as a bathtub-shaped failure rate, which is suitable for modeling the lifespan of patients with an increased risk of death. Some basic and dynamic properties of the model are examined. Four methods for estimating its parameters are discussed, and a simulation study is used to examine the consistency and efficiency of these estimators. Finally, the usefulness of the proposed model is demonstrated in the analysis of some data sets. [ABSTRACT FROM AUTHOR]

This paper aims to find the actuarial tables that best represent the occurrences of mortality and disability in the Brazilian Armed Forces, thus providing a better dimensioning of the costs of military pensions to be paid by the pension system. To achieve this goal, an optimization software was developed that tests 53 actuarial tables for the death of valid military personnel, 21 boards for entry into the disability of assets, and 21 boards for mortality of invalids. The software performs 199 distinct adherence tests for each table analyzed through linear aggravations and de-escalations in the probabilities of death and disability. The statistical–mathematical method used was the chi-square adherence test in which the selected table is the one with the null hypothesis "observed data" equal to the "expected data" with the highest degree of accuracy. It is expected to bring a significant contribution to society, as a model of greater accuracy reduces the risk of a large difference between the projected cost and the cost observed on the date of the year, thus contributing to the maintenance of public governance. Additionally, the unprecedented and dual nature of the methodology presented here stands out. As a practical contribution, we emphasize that the results presented streamline the calculation of actuarial projections, reducing by more than 90% the processing times of calculations referring to actuarial projections of retirees from the armed forces. As a limitation of the study, we emphasize that, although possibly replicable, the database was restricted only to the Brazilian Armed Forces. [ABSTRACT FROM AUTHOR]

This article comments on the paper "Less-expensive long-term annuities linked to mortality, cash and equity" by Kevin Fergusson and Eckard Platen, appearing in this issue of the Annals of Actuarial Science. It adds two perspectives to their thought-provoking contribution. The first is a similarity to some recent work in quantitative finance on "deep hedging" that leverages machine learning models to find the cheapest replication strategy for a derivative payoff in a largely model-free setting. The second perspective engages with some of the interesting implications of their approach and draws parallels to literature in asset pricing and macro-finance. These perspectives point to the potential need for more fundamental shifts than the authors of the paper are advertising. [ABSTRACT FROM AUTHOR]

The Capitation Payment Unit (CPU) financing mechanism constitutes more than 70% of health spending in Colombia, with a budget allocation of close to 60 trillion Colombian pesos for the year 2022 (approximately 15.7 billion US dollars). This article estimates actuarially, using modern techniques, the CPU for the contributory regime of the General System of Social Security in Health in Colombia, and compares it with what is estimated by the Ministry of Health and Social Protection. Using freely available information systems, by means of statistical copulas functions and artificial neural networks, pure risk premiums are calculated between 2015 and 2021. The study concludes that the weights by risk category are systematically different, showing historical pure premiums surpluses in the group of 0–1 years and deficits (for the regions normal and cities) in the groups over 54 years of age. [ABSTRACT FROM AUTHOR]

The Gompertz–Makeham (GM) distribution, which is used commonly to represent lifetimes based on laws of mortality, is one of the most popular choices for mortality modeling in the field of actuarial science. This paper investigates ordering properties of the smallest and largest lifetimes arising from two sets of heterogeneous groups of insurees following respective GM distributions. Some sufficient conditions are provided for comparing the smallest and largest lifetimes from two sets of dependent variables in the sense of usual stochastic ordering. Comparison results on the smallest lifetimes, in the sense of hazard rate ordering and ageing faster ordering, are established for two groups of heterogeneous independent lifetimes. Under a similar set-up, no reversed hazard rate ordering is shown to exist between the largest lifetimes with the use of a counter-example. Finally, sufficient conditions are presented for comparing two sets of independent heterogeneous lifetimes under random shocks by means of usual stochastic ordering. Such comparisons for the smallest lifetimes are also carried out in terms of hazard rate ordering. [ABSTRACT FROM AUTHOR]

The Burr Type XII distribution is commonly used in reliability analysis, survival analysis, and actuarial science to model the time-to-failure of a system or component. It is also used in finance to model the distribution of portfolio returns and in hydrology to model the frequency of extreme events. In this work, a new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based construction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations. [ABSTRACT FROM AUTHOR]