Howard R. Waters

Some Optimal Dividends Problems

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

Recursive Calculation of Survival Probabilities

AbstractIn this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

Reinsurance and ruin

Abstract We study the effect of reinsurance on the probability of ultimate ruin in the classical surplus process and consider a retention level as optimal if it minimises the ruin probability. We show that optimal retention levels can be found when the reinsurers premium loading depends on the retention level. We also show that when the aggregate claims process is approximated by a translated Gamma process, very good approximations to both optimal retention levels and ruin probabilities can be obtained. Finally, we discuss the effect of reinsurance on the probability of ruin in finite time.

SOME STABLE ALGORITHMS IN RUIN THEORY AND THEIR APPLICATIONS

In this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions.

Longevity in the 21st Century

The main objective of this paper is to offer a detailed analysis of mortality change in the United Kingdom at the beginning the 21st century. Starting from an exploration of 20th century mortality trends, focusing in particular on the 1990s, underlying forces driving trends in longevity are discussed. These include the ‘cohort effect’ and the ‘ageing of mortality improvement’. International mortality statistics and trends are also analysed. The pace of medical advances is discussed, with specific focus on research into the ageing process and a potential treatment for cardiovascular disease. The paper also discusses the potential threat from infectious diseases.

The Probability and Severity of Ruin in Finite and Infinite Time

In this paper we present algorithms to calculate the probability and severity of ruin in both finite and infinite time for a discrete time risk model. We show how the algorithms can be applied to give approximate values for the same quantities in the classical continuous time risk model.

Some mathematical aspects of reinsurance

Abstract In two earlier papers, Waters (1979) and Andreadakis and Waters (1980), the effect on an insurer as a result of varying his retention limits has been studied. This present paper represents an extension of this earlier work. In particular we investigate whether it is possible to prove some of the results of the earlier papers without making restrictive assumptions about the distribution of annual claims or about the way in which the reinsurance premium is calculated. It will be shown that this is possible in the case of proportional but not possible in the case of non-proportional reinsurance.

The Genetics of Breast and Ovarian Cancer I: A Model of Family History

We present a Markov model of breast cancer (BC) and ovarian cancer (OC) and estimate its transition intensities, mainly using United Kingdom population data. In the case of BC and OC, we estimate intensities according to BRCA1 and BRCA2 genotype. We use this to estimate the probabilities that an applicant for insurance has a BRCA1 or BRCA2 mutation, given complete or incomplete knowledge of her family history of BC and OC. Life (and other) insurance underwriters typically have incomplete knowledge of family history, for example no information on the number of healthy relatives. We show how these probabilities depend strongly on estimates of the mutation frequencies and penetrances, and conclude that it may not be appropriate to apply risk estimates based on studies of high-risk families to other groups.

Ruin probabilities allowing for delay in claims settlement

Abstract In this paper we use martingale techniques to derive upper bounds for the probability of ruin for a risk process. The important difference between our results and previous results in this area is that our model for the risk process explicitly allows for delay in claims settlement.

The genetics of breast and ovarian cancer II:A model of critical illness insurance

We present a model of breast cancer (BC) and ovarian cancer (OC) and other events that would lead to a claim under a Critical Illness (CI) insurance policy, and estimate its transition intensities, mainly using United Kingdom population data. We use this to estimate the costs of CI insurance in the presence of a family history of BC or OC, using the probabilities from Part I of carrying a BRCA1 or BRCA2 mutation, given the family history. In practice, the family history may not include all relevant facts; we look at the range of costs depending on what is known. We show the effect of lower penetrance than is observed in high-risk families. Finally, we consider what the cost of adverse selection might be, were insurers unable to use genetic test or family history information.