Steven Haberman

• MA, PhD, DSc
• Professor at City, University of London

In recent decades, analysing the progression of mortality rates has become very important for both public and private pension schemes, as well as for the life insurance branch of insurance companies. Traditionally, the tools used in this field were based on stochastic and deterministic approaches that allow extrapolating mortality rates beyond the...

Evidence from panel surveys of households, collected over several years and in different countries , shows that people's perception about their remaining lifetime deviates from actuarial data. This has consequences for consumption, savings and investment over an individual's financial life cycle, and in particular for retirement planning and the pu...

It is well known that more advantaged socio-economic groups – whether defined by educational attainment, occupation, income or area deprivation – have lower mortality rates and longer lives than less advantaged socio-economic groups. In many cases, affluent subpopulations also experience faster rates of improvement in mortality. Socio-economic diff...

We introduce a compositional power transformation, known as an {\alpha}-transformation, to model and forecast a time series of life-table death counts, possibly with zero counts observed at older ages. As a generalisation of the isometric log-ratio transformation (i.e., {\alpha} = 0), the {\alpha} transformation relies on the tuning parameter {\alp...

Like density functions, period life-table death counts are nonnegative and have a constrained integral, and thus live in a constrained nonlinear space. Implementing established modelling and forecasting methods without obeying these constraints can be problematic for such nonlinear data. We introduce cumulative distribution function transformation...

Age‐specific life‐table death counts observed over time are examples of densities. Nonnegativity and summability are constraints that sometimes require modifications of standard linear statistical methods. The centered log‐ratio transformation presents a mapping from a constrained to a less constrained space. With a time series of densities, foreca...

While the solvency analysis of immediate life annuity portfolios has been extensively studied, the case of deferred annuities has received comparatively much less attention. We assess the importance and effect of stochastic mortality models and interest rates on the solvency analysis of a portfolio of deferred annuity contracts. Our analysis consid...

For the life insurance industry and pension schemes, mortality projections are critical for accurately managing exposure to longevity risk in terms of both premium setting and reserving. Frailty has been identified as an important latent factor underpinning the evolution of mortality rates. It represents the comorbidities that drive the deteriorati...

The analysis of residual life expectancy evolution at retirement age holds great importance for life insurers and pension schemes. Over the last 30 years, numerous models for forecasting mortality have been introduced, and those that allow us to predict the mortality of two or more related populations simultaneously are particularly important. Inde...

In the actuarial literature, frailty is defined to be the unobserved variable which encompasses all the factors affecting human mortality other than gender and age. Heterogeneity in individual frailty can play a significant role in population mortality dynamics. In the present paper, we identify the main latent factors that explain the frailty comp...

Mortality patterns experienced in closely related populations show similarities in some aspects and differences in others. Indeed, if a decline in mortality rates among low-mortality countries is observed, it is possible that populations experience different trends through which this decline occurs. Observing mortality rates for ages and over speci...

The starting point of our research is the inadequacy of assuming, in the construction of a model of mortality, that frailty is constant for the individuals comprising a demographic population. This assumption is implicitly made by standard life table techniques. The substantial differences in the individual susceptibility to specific causes of deat...

The main objective of this article is to identify significant mortality drivers in the U.S. population that have a high likelihood of being linked to the historical improvement or deterioration of mortality over the 1959 to 2016 period. To achieve this objective, we integrate cause of death modeling with epidemiological evidence to explain the unde...

Decomposition methods are a standard tool used by demographers to understand and communicate the contribution of different factors to the evolution of demographic metrics. Despite their widespread use in demography, decomposition methods are less commonly used by actuaries. In this paper we develop a new approach for decomposing mortality improveme...

The starting point of our research is the inadequacy of assuming, in the construction of a model of mortality, that frailty is constant for the individuals comprising a demographic population. This assumption is implicitly made by standard life table techniques. The substantial differences in the individual susceptibility to specific causes of deat...

The Covid-19 pandemic caused an alarming mortality stress. The evidence shows that a significant proportion of people who die from Covid-19 are in a frail state. According to this consideration, we assume that the mortality shocks are related to a group of the individuals with some co-morbidities at Covid-19 diagnosis. In other words, the mortality...

Mortality rates have been falling or ‘improving’ in many demographically developed countries since the 1950s. However, there has been a slowdown since 2010 in the speed of improvement and this phenomenon has been particularly marked at ages over 50. To understand better this mortality slowdown, we have analysed long-run mortality trends of a group...

When modelling the age distribution of death counts for multiple populations, we should consider three features: (1) how to incorporate any possible correlation among multiple populations to improve point and interval forecast accuracy through multi-population joint modelling; (2) how to forecast age distribution of death counts so that the forecas...

A common feature in the modelling and extrapolation of the trends in mortality rates over time, based on fitted parametric structures, has tended to involve the treatment of a structured fitted main effects period component (with possibly a cohort component) as a random effects time series. In this paper, we follow the lead of Haberman and Renshaw...

The demographic, economic and social changes that have characterized the last decades, and the dramatic financial crisis that has taken place since 2008, have led to a demand for structural changes in the pension sector and a growing interest in individual pension products. Hence the need, for most elderly people, to liquidate their fixed assets, w...

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvemen...

The use of a gender-neutral annuity divisor introduces an intra-generational redistribution from short-lived towards long-lived individuals; this entails a transfer of wealth from males to females and from low socioeconomic groups to high socioeconomic groups. With some subpopulations consisting of females from low socioeconomic groups (or males fr...

An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality forecasts based on a partial age-range model. On the other hand, with all availa...

An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can be taken place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality forecasts based on a partial age-range model. On the other hand, with all av...

In pay-as-you go pension systems, automatic balancing mechanisms (ABMs) are designed to face adverse demographic and economic changes. In this respect, ABMs can be defined as a set of pre-determined measures established by law to be applied immediately as required according to an indicator that reflects the financial health of the system. The purpo...

In this paper, we formulate the multi-population mortality forecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sam...

When modelling subnational mortality rates, we should consider three features: (1) how to incorporate any possible correlation among subpopulations to potentially improve forecast accuracy through multi-population joint modelling; (2) how to reconcile subnational mortality forecasts so that they aggregate adequately across various levels of a group...

When modeling sub-national mortality rates, we should consider three features: (1) how to incorporate any possible correlation among sub-populations to potentially improve forecast accuracy through multi-population joint modeling; (2) how to reconcile sub-national mortality forecasts so that they aggregate adequately across various levels of a grou...