This paper considers the modelling of claim durations for existing claimants under income protection insurance policies. A claim is considered to be terminated when the claimant returns to work. Data used in the analysis were provided by the Life and Risk Committee of the Institute of Actuaries of Australia. Initial analysis of the data suggests the presence of a long-run probability, of the order of 7%, that a claimant will never return to work. This phenomenon suggests the use of mixed parametric regression models as a description of claim duration which include the prediction of a long-run probability of not returning to work. A series of such parametric mixture models was investigated, and it was found that the generalised F mixture distribution provided a good fit to the data and also highlighted the impact of a number of statistically significant predictors of claim duration.

In recent years, Constant Proportion Portfolio Insurance (CPPI) has been the most widely recognised form of portfolio insurance among market practitioners, despite a lack of theoretical framework to support it. This paper presents a revised formulation of Option Based Portfolio Insurance (OBPI) and shows, through a case study, how it can be used as a structured product and applied in practice as a dynamic investment strategy for insurance and pensions funds such as with-profits funds. CPPI and the Revised Option Based Portfolio Insurance (ROBPI) technique adopted in this paper are similar in the sense that they rely on dynamic allocation between risky and risk-free assets to provide downside protection. Comparison between the two methods shows that ROPBI is more efficient and forward looking, giving more information about downside risk and producing less volatile asset allocation, which reduces transaction costs and any market impact.

In Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimates.

A formal definition of investment risk in actuarial investigations is given. Case studies estimating the investment risk associated with different investment strategies for defined benefit pension funds using historic market data are presented. It is shown that a few decades ago, when bond markets only extended in depth to 20-year maturities, the investment risk of investing in equities was of the same order of magnitude as the investment risk introduced by the duration mismatch from investing in bonds for immature schemes. It is shown that now, with the extension of the term of bond markets and introduction of strippable bonds, the least risk portfolio for the same pension liability is a bond portfolio of suitable duration. It is argued that investment risk voluntarily undertaken in defined benefit pension plans has grown markedly in recent decades, at a time when the ability to bear the investment risk has diminished. Investment risk in pension funds is quite different to investment risk for other investors, which leads to the possibility that current portfolios are not optimised — that is, there exist portfolios which increase the expected surplus without increasing risk. The formalising of our intuitive concept of investment risk in actuarial applications is a first step in the identification of more efficient portfolios.

In the classical risk model, we use probabilistic arguments to write down expressions in terms of the density function of aggregate claims for joint density functions involving the time to ruin, the deficit at ruin and the surplus prior to ruin. We give some applications of these formulae in the cases when the individual claim amount distribution is exponential and Erlang(2).

This paper briefly examines the options for reform proposed by the Pensions Commission in 2004 to sustain the United Kingdom state pension system in response to an ageing population. It further explores, under various scenarios, the long-term viability of immigration as an alternative policy response, by developing a population projection model to determine the replacement migration levels which would be required to maintain contributions (taxes) at current levels, using population data and assumptions in the public domain. The economic and social implications of immigration-based policies are also considered. This paper does not consider the specific policy recommendations in the Commission's Second Report published in autumn 2005, which at the time of writing was undergoing an internal consultation process.

The results indicate that not only does each policy option proposed by the Pensions Commission require changes which are too large for the policy to be implemented on its own, but that a combination of options is likely to require discomforting changes at the individual level when considered under plausible scenarios. Economic and social implications aside, the results also indicate that immigration is an inefficient and ineffective way of mitigating demographic ageing. The required replacement migration levels are abnormally high and too volatile for it to be considered as a viable policy alternative.

The paper concerns the interest risk management of insurance companies or banks. Classes of stochastic order relations for arbitrary discrete random variables are used to find extremal strategies of immunisation in the context of deterministic immunisation theory. In a special case, the results obtained by Hürlimann (2002) are extended to conditions for immunisation under arbitrary S-convex or S-concave shift factors of the term structure of interest rates. The notion of the Shiu measure is generalised to an immunisation risk measure, accounting for more moments of the asset and liability risks.

Current methods in credibility theory often rely on parametric models, e.g., a linear function of past experience. During the last decade, the existence of high speed computers and statistical software packages allowed the introduction of more sophisticated and flexible modelling strategies. In recent years, some of these techniques, which made use of the Markov Chain Monte Carlo (MCMC) approach to modelling, have been incorporated in credibility theory. However, very few of these methods made use of additional covariate information related to risk, or collection of risks; and at the same time account for the correlated structure in the data. In this paper, we consider a Bayesian nonparametric approach to the problem of risk modelling. The model incorporates past and present observations related to risk, as well as relevant covariate information. This Bayesian modelling is carried out by sampling from a multivariate Gaussian prior, where the covariance structure is based on a thin-plate spline. The model uses the MCMC technique to compute the predictive distribution of future claims based on available data.

The aim of automatic fraud detection is to assist claims handlers by selecting claims which are potentially fraudulent. Such methods must be based on information routinely available. The present paper makes use of logistic regression and the validity of these models as demonstrated on fresh data from household and motor insurance. A second contribution is a strategy for selecting claims that should receive further attention.

From 1870, in the United Kingdom, a generally liberal legal framework for life insurance existed which commanded wide support, particularly from the actuarial profession. Despite its apparent liberalism, however, it is likely that the regulatory framework impeded market entry, particularly of mutual companies. The liberal framework broke down in a number of incremental steps from 1946. This paper traces the development of U.K. life assurance regulation for 101 years from the mid-Victorian period, analyses contemporary reflections on the legal framework within the actuarial profession, and examines the appropriateness of the legal framework for achieving specific economic objectives for long-term insurance regulation.

Hereditary nonpolyposis colorectal cancer (HNPCC) is characterised by the familial aggregation of cancer of the colon and rectum (CRC). It may be caused by any of five mutations in DNA mismatch repair (MMR) genes or by non-genetic factors, such as life style. However, it accounts for only about 2% of CRC, which is a very common cancer. Previous actuarial models, of diseases with only genetic causes, assumed that a family history of the disease shows mutations to be present, but this is not true of HNPCC. This is a significant limitation, since the best information available to an underwriter (especially if the use of genetic test results is banned) is likely to be knowledge of a family history of CRC. We present a Markov model of CRC and HNPCC, which includes the presence of a family history of CRC as a state, and estimate its intensities allowing for MMR genotype. Using this we find the MMR mutation probabilities for an insurance applicant with a family history of CRC. Our model greatly simplifies the intensive computational burden of finding such probabilities by integrating over complex models of hidden family structure. We estimate the costs of critical illness insurance given the applicant's genotype or the presence of a family history. We then consider what the cost of adverse selection might be, if insurers are unable to use genetic tests or family history information. We also consider the effect of using alternative definitions of a family history in underwriting.

The implications of genetic testing information availability for society, medicine, employment, and individual privacy rights have generated much political debate, legislation and academic research. Part of this debate centres on the ethical and economic considerations resultant from this expanded knowledge, particularly for insurance practices. Within insurance economics, the possibility of adverse selection has been debated and the potential for a ban on an insurer's use of genetic testing has been studied with respect to whether or not such a ban might actually result in insurance market failure due to this adverse selection. Studies have examined the issue using expected loss cost (actuarial or ‘fair’) pricing models, and have not considered either equilibrium (supply and demand) price setting as is present in markets, or the potentially swamping effect of background health care risks facing the insured, having nothing to do with any particular genetic mutation. Here we construct a supply and demand function with both high and low risk individuals in the presence of background health care cost risks, and derive an equilibrium price and market composition to determine whether, if genetic information is allowed for individuals, but this same information is not shared with insurers: (1) is market failure inevitable? (it is not if the background risk is sufficiently high relative to potential genetic risk costs); (2) will equilibrium prices result in all low risk insured exiting the market? (not in the presence of significant background risk); and (3) how much would prices increase and market sales decrease if insurers do not have the same genetic information as the insured? (prices will increase, but not necessarily very much in the presence of background risk, and not as much as that previously estimated in the insurance literature).

This paper is intended to illustrate the adaptive control approach in insurance. A zone-adaptive control strategy harmonising the requirements of principles of solvency and equity is considered in the simplistic framework of a diffusion multiperiodic risk model. Other works by the author set similar adaptive control strategies in a more realistic Poisson-exponential multiperiodic risk model. There is much scope for further generalisations.

A.A.S. 1, 319-343 (2007)

Application of a Polygenic Model of Breast and Ovarian Cancer to Critical Illness Insurance