British Actuarial Journal 

About: British Actuarial Journal is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Pension & Risk management. It has an ISSN identifier of 1357-3217. Over the lifetime, 413 publications have been published receiving 6143 citations.

Stochastic Claims Reserving in General Insurance

Abstract: This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.

More on a Stochastic Asset Model for Actuarial Use

Abstract: In this paper the ‘Wilkie investment model’ is discussed, updated and extended. The original model covered price inflation, share dividends, share dividend yields (and hence share prices) and long-term interest rates, and was based on data for the United Kingdom from 1919 to 1982, taken at annual intervals. The additional aspects now covered include: the extension of the data period to 1994 (with omission of the period from 1919 to 1923); the inclusion of models for a wages (earnings) index, short-term interest rates, property rentals and yields (and hence property prices) and yields on index-linked stock; consideration of data for observations more frequently than yearly, in particular monthly data; extension of the U.K. model to certain other countries; introduction of a model for currency exchange rates; extension of certain aspects of the model to a larger number of other countries; and consideration of more elaborate forms of time-series modelling, in particular cointegrated models and ARCH models.

Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities

Abstract: This paper addresses the problem of longevity riskthe risk of uncertain aggregate mortalityand discusses the ways in which life assurers, annuity providers and pension plans can manage their exposure to this risk. In particular, it focuses on how they can use mortality- linked securities and over-the-counter contractssome existing and others still hypothetical ˆ to manage their longevity risk exposures. It provides a detailed analysis of two such securities ˆ the Swiss Re mortality bond issued in December 2003 and the EIB/BNP longevity bond announced in November 2004. It then looks at the universe of hypothetical mortality-linked securitiesother forms of longevity bonds, swaps, futures and optionsand investigates their potential uses. It also addresses implementation issues, and draws lessons from the experiences of other derivative contracts. Particular attention is paid to the issues involved with the construction and use of mortality indices, the management of the associated credit risks, and possible barriers to the development of markets for these securities. It suggests that these implementation difficulties are essentially teething problems that will be resolved over time, and so leave the way open to the development of flourishing markets in a brand new class of securities.

The Cohort Effect: Insights and Explanations

Abstract: The purpose of the report is to achieve a greater understanding of the United Kingdom ‘cohort effect’ by exploring research in other fields and analysing population mortality data by cause of death in more detail. The ‘cohort effect’ in this context is the observed phenomenon that people born in the U.K. between 1925 and 1945 (centred on the generation born in 1931) have experienced more rapid improvement in mortality than generations born either side of this period.In a Continuous Mortality Investigation (CMI) Bureau working paper published in 2002, a similar trend was noted in the mortality experience of male pensioners and males with life assurance policies. The CMI Bureau investigation showed peak rates of improvement for the cohort born in 1926. Interim projection bases for future mortality experience were produced as a result of the study. The projections made various assumptions about the extent to which the observed cohort effect would continue to shape the pattern of future mortality improvement.This report suggests that it is highly likely that the cohort effect has been caused by a number of different factors in combination. Prevalence of smoking from one generation to the next has certainly been one such factor. Furthermore, an analysis of patterns of cigarette smoking suggests that there is a degree of inevitability in some element of likely future improvement, especially for mortality at older ages from conditions strongly linked to smoking.However, trends in heart disease and breast cancer mortality suggest that smoking is not the only factor. The differences between lung cancer and heart disease trends by year of birth are especially interesting. The report shows that there are two ‘sub-cohorts’ of the 1925 to 1945 cohort: an earlier group where the improvements may be largely due to smoking; and a later one where other factors, such as diet in early life, may have played a greater role.Historic patterns of smoking behaviour by socio-economic class provide an explanation for the five-year difference in the year of birth showing the fastest improvements, i.e. the difference between 1926 for the CMI Bureau investigation and 1931 for the general population. It is also notable that the second ‘sub-cohort’ of high improvement, applying to people born in the early 1940s, can be seen in both population and CMI experience.A case study examining Japanese mortality experience shows that strong cohort trends can be projected well into old age. This does not provide proof that the U.K. cohort effect will do the same. However, it does counter arguments that year of birth effects will inevitably wear off with age. It is especially interesting given recent epidemiological research linking early life experience with markers of ageing.There are a number of reasons to believe that the U.K. cohort effect will have an enduring impact on rates of mortality improvement in future decades. These include historical patterns of smoking behaviour and the impact of early life experience on health in later life. There appears to be little evidence to support the idea that the width of the generation experiencing rapid improvement will reduce with time.

A Stochastic Model Underlying the Chain-Ladder Technique

Abstract: This paper presents a statistical model underlying the chain-ladder technique. This is related to other statistical approaches to the chain-ladder technique which have been presented previously. The statistical model is cast in the form of a generalised linear model, and a quasi-likelihood approach is used. It is shown that this enables the method to process negative incremental claims. It is suggested that the chain-ladder technique represents a very narrow view of the possible range of models.