Actuarial Science Research Articles

Roles and Scenario of Partly Qualified Actuaries in Insurance Companies of Nepal

The field of actuarial science uses mathematical and statistical techniques to evaluate financial risks in the insurance and finance industries. Actuaries are creative, curious and adaptable human resources and problem solvers, who need to possess different skills and knowledge to solve risk related problems. Partly Qualified Actuaries (PQA) is semi-professionals actuary. From analyzing the financial costs of risk and uncertainty to pricing and reserving, partly qualified actuaries are important in doing the basic to advanced actuarial tasks in these businesses. The research paper investigates on the role of partly qualified actuaries in the insurance industry in Nepal and analyzes the factors impacting the role of PQA in Nepalese insurance companies. The objective of this study is to look into the scenario and important role of Partly Qualified Actuary in the insurance companies. Descriptive and analytical research design was used in this study. The data collected through questionnaire from100 respondents was used for analysis from PQA, insurance companies' staffs, policy makers and some academicians of Nepal who are well informed about actuary. The research shows that the number of PQA is increasing in Nepal every year and they are working in different insurance companies.

Bridging the gap from the current deposit insurance fund to a fund target

We use ruin theory, as developed in actuarial science, to study the impact of deposit insurer choices for insurance pricing, funding (capitalization), resolving bank failures and managing investments on the probability of insurer insolvency. We use a risk aggregation model (copula) to combine multiple insurer revenue and expense streams to determine the optimum (target) deposit insurance fund level. Next, we apply ruin theory to different strategies for achieving the target fund through simulated revenue and expense streams and show how these strategies affect the probability of deposit insurer insolvency. For our empirical estimates we use the U.S. Federal Deposit Insurance Corporation’s annual revenues and expenses as a case study. Our results suggest that ruin theory can provide insights about how deposit insurer’s choices for pricing deposit insurance, funding, resolving bank failures and managing investments affect the risk of insurer insolvency. Further, our analysis demonstrates the interactions of key insurance operations on insurer risk, with the implication that deposit insurers should manage these operations jointly rather than independently, as characterized by deposit insurance laws and the academic literature.

Is designed data collection still relevant in the big data era? – A discussion

Is designed data collection still relevant in the big data era? – A discussion

On composite length-biased exponential-Pareto distribution: Properties, simulation, and application in actuarial science

The composite length-biased exponential-Pareto (CLBEP) distribution is a new composite distribution that is introduced in this article. This model's probability density function, moments, and quantiles, among other statistical characteristics, are determined mathematically. The parameters' maximum-likelihood estimation and stochastic ordering are discussed. A comparison study with other new composite and conventional distributions is also included. Specifically, using two actual fire insurance data sets, the goodness of fit of this new model is contrasted with the composite exponential-Pareto, composite lognormal-Pareto, and composite Rayleigh-Pareto distributions (Algerian and Danish fire insurance losses).2010 AMS subject classifications62E10; 60E05.

Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms

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.

Prediction Interval for Compound Conway–Maxwell–Poisson Regression Model with Application to Vehicle Insurance Claim Data

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.

A Modified Gamma Model: Properties, Estimation, and Applications

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.

Benchmarks for the benchmark approach to valuing long-term insurance liabilities: comment on Fergusson & Platen (2023)

AbstractThis 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 theAnnals 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.

Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences

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.

Preference robust distortion risk measure and its application

AbstractDistortion 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.

Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons

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.

A Tweedie Compound Poisson Model in Reproducing Kernel Hilbert Space

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 (https://cran.r-project.org/package=ktweedie).

An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data

<abstract> <p>Time series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other distributions such as the generalized Poisson, double Poisson, hyper-Poisson, and COM-Poisson distributions have been proposed to replace the Poisson distribution to model the different levels of dispersion in time series of counts. These models have certain limitations such as complex expressions for the mean and variance which complicate the formulation as GARCH models. In this study, we propose an alternative hyper-Poisson (AHP) distribution, with simple forms of conditional mean and variance, for an integer-valued GARCH (INGARCH) model for time series of counts that also exhibit the different levels of dispersion. We demonstrate that the AHP-INGARCH model is comparable to some existing INGARCH models. Additionally, the model can cover a wider range of dispersion. The maximum likelihood estimation can be used to estimate the parameters of the proposed model. Applications to three real-life data sets related to polio, internet protocol and daily COVID-19 new deaths underscore the usefulness of the proposed model in studying both over-dispersed and under-dispersed time series of counts.</p> </abstract>

Deep Learning Incorporated Bühlmann Credibility in the Modified Lee–Carter Mortality Model

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.

Optimization of medical insurance actuarial based on biometric data

Only a detailed study of the insured in long-term health insurance can better avoid risks and further serve the insured. Biostatistics is a discipline that applies the principles and methods of statistics to study life sciences, reveals the inevitable laws in a large number of random phenomena from the quantitative aspect, and is the application of probability theory and mathematical statistics in the biological field. The research results provide new ideas and methods for actuarial science of social health insurance in China.

A goodness-of-fit test for the compound Poisson exponential model

On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.

Introduction to Actuarial Science and the Actuary Profession at SMA PRAMITA Tangerang

Actuarial science is a science that applies mathematical and statistical science methods to assess risk. Currently actuaries are needed with large income. But ironically, many high school students do not know the knowledge and profession of actuaries. Community service activities are carried out as an actualization of knowledge from the Statistics Study Program at Matana University through an introductory seminar on actuarial science and the actuary profession given to Class X students of PRAMITA SMA Tangerang. Community service can be carried out very well. Positive responses from all seminar participants included the level of satisfaction (satisfied 11.6%, very satisfied 46.5% and very satisfied 41.9%), the usefulness of the event (100% useful), and the quality of the program (9.3 % good, 39.5% very good, 51.2% very good). This PKM activity is an implementation of the Mathematical Finance and Insurance Mathematics courses.

Optimal Retention for Uncertain Stop-Loss Reinsurance Model

The optimal reinsurance is one of the important issues in actuarial science. In this paper, we discuss the optimal stop-loss reinsurance problem in uncertain environment. An uncertain optimal stop-loss reinsurance model is presented, where the reinsurance premium is calculated by expected value principle and the uncertain value-at-risk is chosen as the insurer’s total risk measure. Next, some conditions that the proposed uncertain stop-loss reinsurance model has optimal retention are provided. At last, a few numerical examples are given to illustrate the application.

Closed-form expressions to Gompertz-Makeham life expectancies: a historical note

Results well known in the actuarial community about closed-form expressions to Gompertz and Gompertz-Makeham life expectancies for a person aged x are still being independently rediscovered to this day. This note seeks to acknowledge previous results about closed-form expressions to Gompertz-Makeham life expectancies, especially in the actuarial science field, hoping to stimulate interdisciplinarity and provide the background for further developments, especially since the derivation of closed-form expressions for life expectancy (and annuities) based on particular mortality laws are matters of interest for multiple fields such as actuarial science, biology, demography, statistics among others.

Parameter Estimation of Exponentiated Half-Logistic Distribution for Left-Truncated and Right-Censored Data

Left-truncated and right-censored data are widely used in lifetime experiments, biomedicine, labor economics, and actuarial science. This article discusses how to resolve the problems of statistical inferences on the unknown parameters of the exponentiated half-logistic distribution based on left-truncated and right-censored data. In the beginning, maximum likelihood estimations are calculated. Then, asymptotic confidence intervals are constructed by using the observed Fisher information matrix. To cope with the small sample size scenario, we employ the percentile bootstrap method and the bootstrap-t method for the establishment of confidence intervals. In addition, Bayesian estimations under both symmetric and asymmetric loss functions are addressed. Point estimates are computed by Tierney–Kadane’s approximation and importance sampling procedure, which is also applied to establishing corresponding highest posterior density credible intervals. Lastly, simulated and real data sets are presented and analyzed to show the effectiveness of the proposed methods.