SOME RESULTS ON OPTIMUM PREMIUM PAYMENT PLANS

Any insurance plan consists of a sequence of payments every year (or some other fixed time interval) in return for certain death benefits. The benefits may take the form of a wide variety of insurances or annuities. For simplicity, we will assume that premiums and benefits are paid annually. In this paper, we investigate the appropriateness of this type of plan. Naturally, appropriateness of any plan cannot be measured without an optimality criteria. Three such criteria, which are statistical in nature, are introduced in this paper. For the principal safety criterion which we use, the optimal premium are those which minimize a certain profit variance subject to a familiar profit constraint. We also develop a profitability criterion and then solve an associated optimality problem. Our main results state that if the sequence of present values of total benefits is nonincreasing, then the profit variance is minimum when the insured pays a net single premium at once, and if this cannot be done, the insured should pay off the policy as early as possible

Applications of Clustering with Mixed Type Data in Life Insurance

Death benefits are generally the largest cash flow item that affects financial statements of life insurers where some still do not have a systematic process to track and monitor death claims experience. In this article, we explore data clustering to examine and understand how actual death claims differ from expected, an early stage of developing a monitoring system crucial for risk management. We extend 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 known mortality. This clustering has the feature to efficiently handle 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 contains observations, during 2014, 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 a 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.Comment: 25 pages, 6 figures, 5 table

A Financial Protection Strategy for Families That Have a Child With Down Syndrome

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

Applications of Clustering with Mixed Type Data in Life Insurance

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