Infant mortality: an insured population perspective

Many insurers offer life coverage to individuals during the first year of life. The policies tend to have small face values, but frequently contain premium waiver or additional purchase options. General population mortality is significantly higher at this age relative to older children and even middle-aged adults. This article presents the mortality experience of an insured cohort in which death occurred under 1 year of age. In summary, the insured population's mortality rate was significantly lower and the leading causes of death were different than the general population.     

Comparison of body mass index and waist circumference as predictors of all-cause mortality in a male insured lives population

Obesity assessed by body mass index (BMI) is associated with increased mortality risk, but there is uncertainty about whether BMI is the best way to measure obesity. Waist circumference (WC) has been proposed as a better measure. The Swiss Re BMI/WC Study was conducted to determine whether BMI or WC is a better predictor of future all-cause mortality in a large male insurance population. Using Cox proportional hazard models, risk ratios for increasing BMI and WC were 1.033 (P < .001) and 1.027 (P < .001), respectively. Risk ratios for obesity defined by BMI > or = 30 kg/m2 and WC > or = 40 inches were 1.33 (P < .001) and 1.20 (P = .002), respectively. In this study, BMI and WC are essentially equivalent in their ability to predict mortality risk in a male insurance population. Obesity, measured by either BMI or WC, has important underwriting and pricing implications.     

Refusal of surgery in an insured population

Among 195 people who did not have recommended elective surgery in which a second opinion was required, virtually all indicated they were not going to have the operation and did not want a second opinion. The extent to which this decision adversely affected their health status and well-being and the extent to which alternate treatments were tried are examined. The findings also highlight the discretionary nature of patient and physician decision making.     

A new parametric model for converting excess mortality from clinical studies to insured population

We propose a new parametric model – the generalized excess mortality (GEM) model – for converting excess mortality from clinical to insured population. The GEM model has been formulated as a generalization of the excess death rate (EDR) model in terms of a single adjustment parameter (m) that accounts for a partial elimination of a clinical study’s EDR due to the underwriting selection process. The suggested value of the parameter m depends only on the ratio of the impairment’s prevalence rate in the insured population to that in the clinical population. The model’s development has been implemented in two phases: the design phase and the validation phase. In the design phase, the data from the National Health and Nutrition Examination Survey I pertaining to three broad impairments (diabetes, coronary artery disease, and asthma) have been used. As a result, the following equation for the parameter m has been proposed: m_k?=?(P_i,k/P_c,k)ⁿ, where P_i,k, P_c,k are the prevalence rates of impairment k under study in the insured and the clinical populations, respectively, and n a single universal parameter with its value best approximated as n?=?0.5 (95% confidence interval 0.5–0.6). In the validation phase, several independent clinical studies of three other impairments (Crohn’s disease, epilepsy, and chronic obstructive pulmonary disease) were used. As it has been demonstrated in the validation phase, for a number of impairments, the GEM model can provide a better fit for observed insured population mortality than either one of the conventional EDR or mortality ratio models.     

Post-war mortality among industrial insured lives in Norway

Abstract

The results of mortality investigations among industrial insured lives with weekly premiums in the Norwegian life insurance company Fram for the period 1931/40 and for the period 1940/46 have earlier been published in this journal.l It is now possible to render the main results of the continued investigation for the post-war years 1946/50.     

The mortality among industrial insured lives in Norway during the war

In the Norwegian life insurance company Fram a continuous mortality investigation takes place in connection with the yearly valuation of policies issued with weekly premiums. The investigation gives the aggregate mortality, the unit is the policy and the year of observation is the calendar year. A detailed account of the method used has been given by Fredrik Borch in his paper: “The mortality among industrial insured lives in Norway 1931–1940” in this journal 1943. The most important results of the investigation from the years 1940–1946 are rendered below.     

The non mortality of hypertrophic cardiomyopathy in an unselected, community diagnosed and treated population

Hypertrophic Cardiomyopathy (HC) is portrayed in past literature as having an ominous prognosis. However, most studies emanated from medical centers and suffered from potential referral bias. A population based, community diagnosed and treated survival study is analyzed by the life table method. Despite potential causes for both underestimation of the observed mortality as well as for overestimation of expected mortality, the study appears to reveal a more favorable prognosis for HC in this population.     

Pricing implications of trends in population mortality and underwriting effectiveness

Pricing actuaries try to anticipate insured lives mortality rates for decades into the future by considering historic relationships between population and insured lives mortality and trends in population mortality. The degree to which underwriting might decrease insured lives mortality relative to population mortality is of particular importance. A comparison of trends in population and insured mortality is presented to illustrate historic relationships. Two theories for future life expectancy trends are: 1) no foreseeable limit to life expectancy, and 2) life expectancy limited by biological forces. Factors that may increase or decrease the future effectiveness of underwriting are reviewed.     

A Bayesian non-parametric model for small population mortality

This paper proposes a Bayesian non-parametric mortality model for a small population, when a benchmark mortality table is also available and serves as part of the prior information. In particular, we extend the Poisson-gamma model of Hardy and Panjer to incorporate correlated and age-specific mortality coefficients. These coefficients, which measure the difference in mortality levels between the small and the benchmark population, follow an age-indexed autoregressive gamma process, and can be stochastically extrapolated to ages where the small population has no historical exposure. Our model substantially improves the computation efficiency of existing two-population Bayesian mortality models by allowing for closed form posterior mean and variance of the future number of deaths, and an efficient sampling algorithm for the entire posterior distribution. We illustrate the proposed model with a life insurance portfolio from a French insurance company.     

Stochastic mortality models: an infinite-dimensional approach

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite-dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvements which provide a flexible tool for a simple construction of stochastic forward mortality models. In practice, the notion of mortality improvements is a convenient device for the quantification of changes in mortality rates over time, and enables, for example, the detection of cohort effects. We show that the forward mortality rates satisfy Heath–Jarrow–Morton-type consistency conditions which translate to conditions on the forward mortality improvements. While the consistency conditions for the forward mortality rates are analogous to the classical conditions in the context of bond markets, the conditions for the forward mortality improvements possess a different structure. Forward mortality models include a cohort parameter besides the time horizon, and these two dimensions are coupled in the dynamics of consistent models of forward mortality improvements. In order to obtain a unified framework, we transform the systems of Itô processes which describe the forward mortality rates and improvements. In contrast to term structure models, the corresponding stochastic partial differential equations (SPDEs) describe the random dynamics of two-dimensional surfaces rather than curves.     

Creation of an Islamic stock index in West Africa

Islamic finance, which has become inescapable has entered into financial markets by offering solutions consistent with the precepts of the Shariah. The objective of this paper is to propose the creation of an Islamic stock index in West Africa. The choice of market values ​​requires extra financial and financial screening system. The results show that 10% of the securities in Nigeria Stock Exchange , the Regional Stock Exchange (Brvm) and the Ghana Stock Exchange (Gse) were selected to form the Islamic index " Ecowas Shariah index.     

Infantile mortality from an actuarial point of view

Abstract

1. The difficulties by which the actuary is confronted in dealing with infantile mortality resemble in several ways the difficulties experienced at extreme old age. In both cases the variation in the mortality is so rapid that the usual formulas of numerical approximation may break down. In both cases the observations of the life insurance companies are scarce, and hypothesis must therefore be resorted to. In both cases there is a question of convergence, if the force of mortality is assumed to tend to infinity, as the age tends to zero. In both cases it is, of course, impossible to tell with certainty whether the force of mortality does actually tend to infinity.