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.

For a portfolio of life insurance policies observed for a stated period of time, e.g., one year, mortality is typically a rare event. When we examine the outcome of dying or not from such portfolios, we have an imbalanced binary response. The popular logistic and probit regression models can be inappropriate for imbalanced binary response as model estimates may be biased, and if not addressed properly, it can lead to serious adverse predictions. In this paper, we propose the use of skewed link regression models (Generalized Extreme Value, Weibull, and Fre\`chet link models) as more superior models to handle imbalanced binary response. We adopt a fully Bayesian approach for the generalized linear models (GLMs) under the proposed link functions to help better explain the high skewness. To calibrate our proposed Bayesian models, we use a real dataset of death claims experience drawn from a life insurance company's portfolio. Bayesian estimates of parameters were obtained using the Metropolis-Hastings algorithm and for Bayesian model selection and comparison, the Deviance Information Criterion (DIC) statistic has been used. For our mortality dataset, we find that these skewed link models are more superior than the widely used binary models with standard link functions. We evaluate the predictive power of the different underlying models by measuring and comparing aggregated death counts and death benefits.

Death benefit claims are generally the largest cash flow item that affects financial statements of life insurance companies. Yet surprisingly, some life insurers do not have a systematic process to track and monitor their portfolios’ death claims. Such a process clearly requires a meticulous investigation of historical death claims experience. In this article, we explore the use of data clustering to examine and understand how actual death claims differ from the expected. This is an important early stage of developing a tracking and monitoring system that is a crucial part of risk management for a life insurer. In particular, we implement the k-prototypes clustering algorithm to draw inference from a life insurance dataset using only the insured’s characteristics and policy information without regard to the known mortality. This clustering algorithm has the feature to efficiently handle both categorical and numerical attributes, which are present in our dataset. The optimal clusters obtained from the proposed algorithm are then used to compare and monitor actual to expected death claims experience of a life insurance portfolio. Our empirical data contains observations, during the third quarter of 2014, of approximately 1.15 million policies with a total insured amount of over 650 billion dollars. For this portfolio, the algorithm produced four natural clusters, with each cluster having a lower actual to expected death claims but with differing variability. The results of our analysis can provide management a process to identify policyholders’ attributes that dominate significant mortality deviations, and thereby enhance decision making for taking necessary precautions or …

In this chapter, we consider the model of call center incoming call forecasting and staffing-level optimization. We first present the structure of the model and how an agent-based modeling technique could enrich the decision rule and the model. A matrix layout is introduced to present the model so that it can be understood in an efficient way from the perspective of a programmer. The agent-based queuing model will be used in forecasting. We then utilize the bisection method and stepwise method to optimize the staff level to satisfy a target range service-level criteria. Call center management could use the model in practice for their management forecasting and optimization decision-making process in terms of how many agents they need to achieve the target business efficiency goal.

Families that have a child with Down syndrome (DS) are facing financial challenges due to the increased life expectancy and daily life dependencies that he or she experiences. This article uses pediatric findings to supplement child mortality impairment assumptions and proposes a combination annuity pricing model to explore an annuity solution for families that have a child with DS. A Markov chain Monte Carlo simulation model is constructed with features such as a fixed death benefit, return of premium, different premium payment patterns, and the widowhood effect factor. The results indicate that such a product is generally affordable for families that have a child with DS to cover their child's longevity risk and increased dependency needs.

In this paper, we define a retrospective accumulated net asset random variable and mathematically demonstrate that its expectation is the retrospective reserve which in turn is equivalent to the prospective reserve. We further explore various properties of this retrospective accumulated net asset random variable. In particular, we find and demonstrate that this retrospective random variable can be used as a tool for helping us extract historical information on the pattern and significance of deviation of actual experience from that assumed for reserving purposes. This information can subsequently guide us as to whether it becomes necessary to adjust prospective reserves and the procedure to do so. The paper concludes, as an illustration, with a model of a block of in force policies with actual experience different from reserving assumptions and a suggested methodology on how prospective reserves could be adjusted based on the realized retrospective accumulated net asset random variable.

In this paper, we define a retrospective loss random variable and mathematically demonstrate that its expectation is the retrospective reserve which in turn is equivalent to the prospective reserve. By defining an associated random variable for the retrospective reserve, similar to the prospective loss random variable for the prospective reserve, we can further explore and understand various properties of this retrospective loss random variable. In particular, we find and demonstrate that this retrospective random variable can be a powerful tool for providing us valuable historical information on the pattern and significance of deviation of actual experience from that assumed for reserving purposes. This valuable information can subsequently guide us as to whether it becomes necessary to adjust prospective reserves and the procedure to do so. The paper concludes with a model of a block of in force policies with actual experience different from reserving assumptions, and a rigorous and consistent methodology on how prospective reserves could be adjusted based on the realized retrospective loss random variable.

There has been some work, e.g.Carriere (1998), Valdez (2000b), and Valdez (2001), leading to the development of statistical models in understanding the mortality pattern of terminated policies. However, there is a scant literature on the empirical evidence of the true nature of the relationship between survivorship and persistency in life insurance. When a life insurance contract terminates due to voluntary non-payment of premiums, there is a possible hidden cost resulting from mortality anti-selection. This refers to the tendency of policyholders who are generally healthy to select against the insurance company by voluntarily terminating their policies. In this article, we explore the empirical results of the survival pattern of terminated policies, using a follow-up study of the mortality of those policies that terminated from a portfolio of life insurance contracts. The data has been obtained from a major insurer which tracked the mortality of their policies withdrawn, for purposes of understanding the mortality anti-selection, by obtaining their dates of death from the Social Security Administration office. We modeled the time until a policy lapses and its subsequent mortality pattern. We find some evidence of mortality selection and we subsequently examined the financial cost of policy termination.