Recent Challenges in Actuarial Science

For centuries, mathematicians and, later, statisticians, have found natural research and employment opportunities in the realm of insurance. By definition, insurance offers financial cover against unforeseen events that involve an important component of randomness, and consequently, probability theory and mathematical statistics enter insurance modeling in a fundamental way. In recent years, a data deluge, coupled with ever-advancing information technology and the birth of data science, has revolutionized or is about to revolutionize most areas of actuarial science as well as insurance practice. We discuss parts of this evolution and, in the case of non-life insurance, show how a combination of classical tools from statistics, such as generalized linear models and, e.g., neural networks contribute to better understanding and analysis of actuarial data. We further review areas of actuarial science where the cross fertilization between stochastics and insurance holds promise for both sides. Of course, the vastness of the field of insurance limits our choice of topics; we mainly focus on topics closer to our main areas of research. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Different Estimation Methods of the Stress-Strength Reliability Restricted Exponentiated Lomax Distribution

Lomax distribution, a large-scale probabilistic distribution used in industry, economics, actuarial science, queue theory, and Internet traffic modeling, is the most important distribution in reliability theory. In this paper estimating the reliability of Restricted exponentiated Lomax distribution in two cases, when one component X strength and Y stress R=P(Y<X), and when system content two component series strength, Y stress by using different estimation method. such as maximum likelihood, least square and shrinkage methods. A comparison between the outcomes results of the applied methods has been carried out based on mean square error (MSE) to investigate the best method and the obtained results have been displayed via MATLAB software package.

A new trivariate model for stochastic episodes

We study the joint distribution of stochastic events described by (X,Y,N), where N has a 1-inflated (or deflated) geometric distribution and X, Y are the sum and the maximum of N exponential random variables. Models with similar structure have been used in several areas of applications, including actuarial science, finance, and weather and climate, where such events naturally arise. We provide basic properties of this class of multivariate distributions of mixed type, and discuss their applications. Our results include marginal and conditional distributions, joint integral transforms, moments and related parameters, stochastic representations, estimation and testing. An example from finance illustrates the modeling potential of this new model.

Machine Learning in P&C Insurance: A Review for Pricing and Reserving

In the past 25 years, computer scientists and statisticians developed machine learning algorithms capable of modeling highly nonlinear transformations and interactions of input features. While actuaries use GLMs frequently in practice, only in the past few years have they begun studying these newer algorithms to tackle insurance-related tasks. In this work, we aim to review the applications of machine learning to the actuarial science field and present the current state of the art in ratemaking and reserving. We first give an overview of neural networks, then briefly outline applications of machine learning algorithms in actuarial science tasks. Finally, we summarize the future trends of machine learning for the insurance industry.

Proxies

Calculating Race’s fourth chapter demonstrates that race has become so highly correlated with other social statistics that actuarial science in general has developed a baked-in racial bias. Racial discrimination by proxy (e.g., zip code standing in for race) can be glimpsed in the disparate impact of data-driven decision-making in housing, healthcare, policing, sentencing, and more. Simply leaving out racial data in statistically aided decision-making distances institutions from claims of intentional discrimination, but a disparate, discriminatory impact lingers when other factors correlated with race power actuarial analyses. Chapter 4 considers how insurance law in the United States has defined the limits of acceptable discrimination. By surveying the progression of state-by-state regulations that prohibit or accept the use of race, gender, sex, sexuality, ability, age, and genetics in an industry that revolves around the ability to discriminate risk, it uncovers who the United States has historically chosen to protect.

Calculating Race

Calculating Race: Racial Discrimination in Risk Assessment presents the historical relationship between statistical risk assessment and race in the United States. It illustrates how, through a reliance on the variable of race, actuarial science transformed the nature of racism and, in turn, helped usher racial disparities in wealth, incarceration, and housing from the nineteenth century into the twentieth. The monograph begins by investigating the development of statistical risk assessment explicitly based on race in the late-nineteenth-century life insurance industry. It then traces how such risk assessment migrated from industry to government, becoming a guiding force in parole decisions and in federal housing policy. Finally, it concludes with an analysis of “proxies” for race—statistical variables that correlate significantly with race—in order to demonstrate the persistent presence of race in risk assessment even after the anti-discrimination regulations won by the Civil Rights Movement. Offering readers a new perspective on the historical importance of actuarial science in structural racism, Calculating Race is a particularly timely contribution as Big Data and algorithmic decision-making increasingly pervade American life.