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.

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.

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.

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 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.