BackgroundChanges of life expectancy over time serve as an interesting public health indicator for medical, social and economic developments within populations. The aim of this study was to quantify changes of life expectancy between 1950 and 2010 and relate these to main causes of death.MethodsPollard’s actuarial method of decomposing life expectancy was applied to compare the contributions of different age- and disease-groups on life expectancy in 5-year intervals.ResultsFrom the 1960 to 70s on, declines in cardiovascular disease (CVD) mortality play an increasing role in improving life expectancy in many developed countries. During the past decades gains in life expectancy in these countries were mainly observed in age groups ≥65 years. A further consistent pattern was that life expectancy increases were stronger in men than in women, although life expectancy is still higher in women. In Japan, an accelerated epidemiologic transition in causes of death was found, with the highest increases between 1950 and 1955. Short-term declines and subsequent gains in life expectancy were observed in Eastern Europe and the former states of the Union of Soviet Socialist Republics (USSR), reflecting the changes of the political system.ConclusionsChanges of life years estimated with the decomposing method can be directly interpreted and may therefore be useful in public health communication. The development within specific countries is highly sensitive to changes in the political, social and public health environment.Electronic supplementary materialThe online version of this article (doi:10.1186/s12963-016-0089-x) contains supplementary material, which is available to authorized users.

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We illustrate how multistate Markov and semi-Markov models can be used for the actuarial modeling of health insurance policies, focusing on health insurances that are pursued on a similar technical basis to that of life insurance. In the first part, we give an overview of the basic modeling frameworks that are commonly used and explain the calculation of prospective reserves and net premiums. In the second part, we discuss the biometric insurance risk, focusing on the calculation of implicit safety margins. We present new results on implicit margins in the semi-Markov model and on biometric estimation risk in the Markov model, and we explain why there is a need for future research concerning the systematic biometric risk.

It is essential for insurance regulation to have a clear picture of the risk measures that are used. We compare different mathematical interpretations of the Solvency Capital Requirement (SCR) definition from Solvency II that can be found in the literature. We introduce a mathematical modeling framework that enables us to make a mathematically rigorous comparison. The paper shows similarities, differences, and properties such as convergence of the different SCR interpretations. Moreover, we generalize the SCR definition to future points in time based on a generalization of the value at risk. This allows for a sound definition of the Risk Margin. Our study helps to make the Solvency II insurance regulation more consistent.