The Metabolic Syndrome and All-Cause Mortality in an Insured Lives Population

Abstract

Metabolic syndrome and its association with mortality have not been studied in insured lives populations. The Swiss Re Study evaluated metabolic syndrome prevalence and associated mortality from all causes and circulatory disease in a cohort of 35,470 predominantly healthy individuals, aged 18–83 years, who were issued life insurance policies between 1986 and 1997. Metabolic syndrome was defined using the National Cholesterol Education Program (NCEP) Expert Panel Adult Treatment Panel (ATP) III guidelines. The NCEP obesity criteria were modified with a prediction equation using body mass index, gender, and age substituted for waist circumference. Adjustments also were made for nonfasting triglyceride and blood glucose values. Risk ratios for policyholders identified with metabolic syndrome were 1.16 (P = .156) for mortality from all causes and 1.45 (P = .080) for mortality from circulatory disease compared with individuals without the syndrome. Risk was proportional to the number of components, or score, of the metabolic syndrome present. Risk ratios for metabolic syndrome score were 1.14 (P < .001) for mortality from all causes and 1.38 (P < .001) for mortality from circulatory disease compared with individuals without metabolic syndrome factors. In both all-cause and circulatory death models, relative risk was highest for the blood pressure risk factor. Based on a modified NCEP definition, increased mortality risk is associated with metabolic syndrome in an insured lives cohort and has life insurance mortality pricing implications.     

An Out-of-Sample Analysis of Investment Guarantees for Equity-Linked Products

Abstract

In this paper we analyze the risk underlying investment guarantees using 78 different econometric models: GARCH, regime-switching, mixtures, and combinations of these approaches. This extensive set of models is compared with returns observed during the financial crisis in an out-of-sample analysis, bringing a new perspective to the study of equity-linked insurance. We find that despite the very good fit of recent models, too few of them are capable of consistently generating low returns over long periods, which were in fact observed empirically during the financial crisis. Moreover, tail risk measures vary significantly across models, and this emphasizes the importance of model risk. Most insurance companies are now focusing on dynamically hedging their investment guarantees, and so we also investigate the robustness of the Black-Scholes delta hedging strategy. We find that hedging errors can be very large among the top fitting models, implying that model risk must be taken into consideration when hedging investment guarantees.     

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.     

Markov Aging Process and Phase-Type Law of Mortality

Abstract

In this article, we propose a finite-state Markov process with one absorbing state to model human mortality. A health index called physiological age is introduced and modeled by the Markov process. Under this model the time of death follows a phase-type distribution. The model possesses many desirable analytical properties useful for mortality analysis. Closed-form expressions are available for many quantities of interest including the conditional survival probabilities of the time of death and the actuarial present values of the whole life insurance and annuity. The heterogeneity or frailty effect of a cohort can be expressed explicitly. The model is also able to explain some stylized facts of observed mortality data. We fit the model to some Swedish population cohort data and life tables compiled by the U.S. Social Security Administration. The fitting results are very satisfactory.     

Household Life Insurance Demand

Abstract

What types of households own life insurance? Who owns term life and who owns whole life insurance? These are questions of great interest to insurers that operate in a highly competitive market. To answer these questions, we jointly examine household demand of two types of insurance, term and whole life, using data from the Survey of Consumer Finances, a probability sample of the U.S. population. We model both the frequency and the severity of demand for insurance, building on the work of Lin and Grace by using explanatory variables that they developed. For the frequency portion, the household decisions about whether to own term and whole life insurance are modeled simultaneously with a bivariate probit regression model. Given ownership of life insurance by a household, the amounts of insurance are analyzed using generalized linear models with a normal copula. The copula permits the bivariate modeling of insurance amounts for households who own both term and whole life insurance, about 20% of our sample. These models allow analysts to predict who owns life insurance and how much they own, an important input to the marketing process.

Moreover, our findings suggest that household demand for term and whole life insurance is jointly determined. After controlling for explanatory variables, there exists a negative relationship for a household’s decision to own both whole and term life insurance (the frequency part) and a positive relationship for the amount of insurance purchased (the severity part). This indicates that the greater the probability of holding one type, the smaller the probability of holding the other type of life insurance. However, higher demand for both types of insurance exists when a household decides to own both. This mixed effect extends prior work that established a negative relationship, suggesting that term life insurance and whole life insurance are substitutes for one another. In contrast, our findings reveal that the ownership decision involves substitution, but, for households owning both types of insurance, amounts are positively related. Therefore, term and whole life insurance are substitutes in the frequency yet complements in the severity.     

Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.