Reverse mortgages provide a mechanism for seniors to release the equity that has been built up in their home. At termination, the mortgagors are usually guaranteed to owe no more than the value of their property. The value of the reverse mortgage guarantee is heavily dependent on the maturity or termination date, which is uncertain. In this paper, we model reverse mortgage terminations using a semi-Markov multiple state model which incorporates three different modes of exit: death, entrance into a long-term care facility, and voluntary prepayment. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages (HECMs) in the USA. We examine the significance of each mode of termination by valuing the contracts allowing progressively for each mode. On the basis of our model and assumptions, we find that both health related terminations and voluntary (non-health related) terminations significantly impact the contract value. In addition we analyze the premium structure for US reverse mortgage insurance, and demonstrate that premiums appear to be too high for some borrowers, and substantial cross-subsidies may result.

This paper analyses the driving forces behind the willingness of South African courts to hear actuarial expert testimony in even the most simple of cases, in contrast to the more circumspect approach of the English courts, when assessing the damages arising out of future loss of earnings following a damage-causing incident. The analysis may well add insight to members of other professions and scientific communities that provide expert testimony to the courts. It is argued that English substantive law of damages and those influenced by its application have something to gain from a consideration of the approach in South Africa.

The claims reserving problem is currently one of the most debated in actuarial literature. The high level of interest in this topic is due to the fact that Solvency II rules will come into operation in 2014. Indeed, it is expected that quantile computations will be compulsory in the evaluation of company risk and for this reason we think that the construction of the claims reserve random variable distribution assumes a fundamental relevance.

The aim of this paper is to present a method for constructing the claims reserve distribution which can take into account IBNyR (Issued But Not yet Reported) claims in a natural way. The construction of the distribution function for each time of the observed interval is done by means of a Monte Carlo simulation model applied on a backward time semi-Markov process. It should be pointed out that this is the first time that a simulation model based on semi-Markov with backward recurrence time has been presented. The method is totally different from the models given in the current literature.

The most important features given in the paper are:

1) for the first time the Monte Carlo simulation method is applied to a backward semi-Markov environment;

2) the Monte Carlo simulation permits the construction of the random variable of the claims reserve for each year of the studied horizon in a natural way;

3) as already pointed out, the backward process attached to the semi-Markov process permits taking into account the evaluation of the IBNyR claims in a natural way.

In the last part of the paper an applicative example constructed from tables that summarise 4 years of claims from an important Italian insurance company will be given.

We consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.

A method is presented for identifying an expected profitable set of customers, to offer them an additional insurance product, by estimating a customer specific latent risk profile, for the additional product, by using the customer specific available data for an existing insurance product of the specific customer. For the purpose, a multivariate credibility estimator is considered and we investigate the effect of assuming that one (of two) insurance products is inactive (without available claims information) when estimating the latent risk profile. Instead, available customer specific claims information from the active existing insurance product is used to estimate the risk profile and thereafter assess whether or not to include a specific customer in an expected profitable set of customers. The method is tested using a large real data set from a Danish insurance company and it is shown that sets of customers, with up to 36% less claims than a priori expected, are produced as a result of the method. It is therefore argued that the proposed method could be considered, by an insurance company, when cross-selling insurance products to existing customers.

We propose a new method for two-dimensional mortality modelling. Our approach smoothes the data set in the dimensions of cohort and age using Bayesian smoothing splines. The method allows the data set to be imbalanced, since more recent cohorts have fewer observations. We suggest an initial model for observed death rates, and an improved model which deals with the numbers of deaths directly. Unobserved death rates are estimated by smoothing the data with a suitable prior distribution. To assess the fit and plausibility of our models we perform model checks by introducing appropriate test quantities. We show that our final model fulfils nearly all requirements set for a good mortality model.

Simulations of a model pension scheme are run with stochastic economic and demographic factors, with an aim to investigate the impact of these factors on movements in funding ratio and average contribution rates. These impacts are analysed by running regressions of movements in funding ratio and average contribution rates against the economic and demographic factors. It is found that, for a typical scheme closed to new entrants and a balanced asset allocation including equity investment, the mismatch between discount rate movements and investment returns is by far the biggest predictor of funding ratio movements, with average contribution rates affected more by events in a few individual years rather than averaged over an entire simulation. Where the scheme invests to cash-flow match liabilities, mortality improvement becomes the most significant predictor of funding ratio movements, although mortality improvement still has little impact on average contribution rates.

This paper argues that most of the problems that actuaries have to deal with in the context of non-life insurance can be usefully cast in the framework of computational intelligence (a.k.a. artificial intelligence), the discipline that studies the design of agents which exhibit intelligent behaviour. Finding an adequate framework for actuarial problems has more than a simply theoretical interest: it also allows a knowledge transfer from the computational intelligence discipline to general insurance, wherever techniques have been developed for problems which are common to both contexts. This has already happened in the past (neural networks, clustering, data mining have all found applications to general insurance) but not systematically, with the result that many useful computational intelligence techniques such as sparsity-based regularisation schemes (a technique for feature selection) are virtually unknown to actuaries.

In this first of two papers, we will explore the role of statistical learning in actuarial modelling. We will show that risk costing, which is at the core of pricing, reserving and capital modelling, can be described as a supervised learning problem. Many activities involved in exploratory analysis, such as data mining or feature construction, can be described as unsupervised learning. A comparison of different computational intelligence methods will be carried out, and practical insurance applications (rating factor selection, IBNER analysis) will also be presented.

This study uses the numeraire portfolio to benchmark insurance stock returns as a natural measure for detecting abnormal insurance stock returns from catastrophic events. The assumptions underlying the efficient markets hypothesis using a numeraire denominated returns approach hold for catastrophic insurance events whereas other more traditional methods such as the market model and Fama-French three factor model often fail, typically due to the accumulation of estimation errors. We construct a portfolio of Australian insurance firms and observe the market reaction to major insured catastrophic events. Using the numeraire denominated returns approach we observe no particular trend in the cumulative abnormal returns of insurance securities following a catastrophic event. Using both the traditional market model and the Fama-French three factor model however, we observe significantly positive cumulative abnormal returns following an insured catastrophic event. The errors inherent in the market model and three factor model for event studies are shown to be eliminated using the numeraire denominated returns approach.

This paper argues that most of the problems that actuaries have to deal with in the context of non-life insurance can be usefully cast in the framework of computational intelligence (a.k.a. artificial intelligence), the discipline that studies the design of agents which exhibit intelligent behaviour. Finding an adequate framework for actuarial problems has more than a simply theoretical interest: it also allows a technological transfer from the computational intelligence discipline to general insurance, wherever techniques have been developed for problems which are common to both contexts. This has already happened in the past (neural networks, clustering, data mining have all found applications to general insurance) but not in a systematic way. One of the objectives of this paper will therefore be to introduce some useful techniques such as sparsity-based regularisation and dynamic decision networks that are not yet known to the wider actuarial community.

Whilst in the first part of this paper we dealt mainly with data-driven loss modelling under the assumption that all the data were accurate and fully relevant to the exercise, in this second part of the paper we explore how to deal with uncertain knowledge, whether this uncertainty comes from the fact that the data are not fully reliable (e.g. they are estimates) or from the fact that the knowledge is “soft” (e.g. expert beliefs) or not fully relevant (e.g. market information on a given risk). Most importantly, we will deal with the problem of making pricing, reserving and capital decisions under uncertainty. It will be concluded that a Bayesian framework is the most adequate for dealing with uncertainty, and we will present a number of computational intelligence techniques to do this in practice.

We use economic indicators to improve the prediction of the number of incurred but not recorded disability insurance claims, assuming that there is a link between the number of claims and the chosen economic indicators. We propose a Bayesian model where we model the claims development in three directions: along incurred periods, recording lag periods and calendar periods. A stochastic model of the economic indicators is incorporated into the calendar period development direction. Thus we allow for the impact of the economic environment on the number of claims. Applying the proposed model to data, we illustrate how the inclusion of economic indicators affects the prediction of the number of incurred but not recorded disability claims.

The purpose of this article is to illustrate how the pension benefits a pension saver will (expect to) receive will depend on the type of pension scheme chosen. We compare three widely different pension savings products: the “traditional” with-profits scheme involving bonus entitlement (average interest rate product), a market-based Unit Link scheme and, finally, a formula based smoothed investment-linked annuity scheme – TimePension in short – which is on many points a cross between the two prior-mentioned types of savings products.

The three product types mentioned above have been analysed in previous literature, but those comparisons were based almost entirely on the values of pension savings accounts at the expiry of the accumulation period. This article will include the payout phase (decumulation phase) in the analysis, enabling us to analyse the size of paid-out pension benefits themselves as well as the possibilities of adjusting these benefits periodically. Compared to earlier articles, we have also improved the underlying model for the uncertainty of the underlying financial market.

The article demonstrates that expected pension benefits from the three schemes are an increasing function of the allocation to shares in the underlying investment portfolios. TimePension involves the highest allocation to shares and therefore offers, on average, the highest pension benefits, followed by the Unit Link scheme. In the third and last place comes the traditional with-profits scheme, which has a relatively low allocation to shares, but which, in return, also provides relatively safe and stable pension benefits. We also show, however, that the stability of pension benefits from a TimePension scheme is completely level with the stability of benefits from the traditional scheme. Unit Link-based pension benefits, on the other hand, vary far more, and pension savers in this product segment will experience much higher annual adjustments – in a both negative and positive direction – than savers in the other product segments.

This paper provides a user-friendly approach to explain how variation in fundamental price-determining variables ‘translates into’ variation in the fundamental value of equities, based on the standard dividend-growth model. The analysis is illustrated with UK data using estimates of real interest rate forecasts and real dividend growth rate forecasts in the past. An important application of this approach is that stock market volatility can be analysed in terms of its component parts. Actual market volatility does not appear to be excessive when compared with the notional volatility implied by changes over time in our estimates of forecast real interest rates and forecast real dividend growth rates.