The conditions under which pension schemes merge is an important issue which has been under-researched. Mergers can affect the strength of the sponsor's covenant and the balance of power between the trustees and the sponsor, as well as the deficit or the surplus of the receiving scheme and its funding ratio. This paper sets out two financial criteria to be met by any pension scheme merger: no profit or loss on merging with another scheme; and no dilution of the funding ratio. After defining a merger basis for valuing the assets and liabilities, and allowing for adjustments to the funding ratio via side receipts and payments; it is shown that, whether or not these criteria are met, depends on the state of the financial markets.

This paper extends the methods introduced in England & Verrall (2002), and shows how predictive distributions of outstanding liabilities in general insurance can be obtained using bootstrap or Bayesian techniques for clearly defined statistical models. A general procedure for bootstrapping is described, by extending the methods introduced in England & Verrall (1999), England (2002) and Pinheiro et al. (2003). The analogous Bayesian estimation procedure is implemented using Markov-chain Monte Carlo methods, where the models are constructed as Bayesian generalised linear models using the approach described by Dellaportas & Smith (1993). In particular, this paper describes a way of obtaining a predictive distribution from recursive claims reserving models, including the well known model introduced by Mack (1993). Mack's model is useful, since it can be used with data sets which exhibit negative incremental amounts. The techniques are illustrated with examples, and the resulting predictive distributions from both the bootstrap and Bayesian methods are compared.

The split capital investment trust crisis brought into focus the need for more reliable risk assessment techniques for shares in the sector. We discuss the strengths and weaknesses of traditional pricing and risk description measures for split capital investment trusts (e.g. gross redemption yield, cover, hurdle rates) and ways of making these more useful. We then examine the application of traditional option pricing techniques and discuss the problems encountered in this approach. Finally, we propose the use of stochastic modelling to deal more effectively with the complexities involved in both pricing shares and understanding their risks.

We investigate the model of Froot & Stein (1998), a model which has very strong implications for risk management. We argue that their conclusions are too strong and need to be qualified. We also argue that their analysis is incorrect and incomplete. Specifically, there are some unusual consequences of their model, which may be linked to the chosen pricing formula.

The International Accounting Standards Board (IASB) is introducing new International Financial Reporting Standards (IFRS) which aim to make financial statements more useful. The process has generated considerable debate. This paper is a contribution to the debate, in the particular context of insurance accounting, and attempts to provide a coherent framework for accounting theory which makes a clear distinction between retrospective statements required for administrative accountability, fair value for current market transactions and to measure value creation, and a prospective prudence required to protect policyholders, depositors and other creditors. It is argued that the IASB's founding purpose to provide a single set of accounts is therefore incoherent; different purposes require different numbers. This also implies that fair value accounts should attempt to value intangible assets. In this context, actuarial analyses of surplus would greatly assist in measuring whether model assumptions are appropriate.

Many recently introduced unit-linked life insurance policies contain provisions allowing policyholders to lapse the product. The problem of pricing this surrender option is difficult as it involves modelling lapse decisions which may be contingent on different factors. This paper develops a methodology which enables us to model lapse behaviour within a framework provided by developments in financial economics. Using marked point processes with stochastic intensities, we present an approach which accounts for changes in the lapse behaviour of policyholders due to different economic factors. As a result, the model produces more accurate financial values for insurance contracts contingent on financial markets. In the context of unit-linked policies, we illustrate the method by allowing the lapse decision to depend on the stochastic volatility of the underlying asset. Our simulation study indicates that there is a strong relation between the single premiums of these policies and the lapse behaviour.

We consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.

This paper examines income inequality over stages of the later-life course (age 45 and older) and systems which can be used to mitigate this inequality. Two hypotheses are tested: (1) levels of income inequality decline during old age because public benefits are more equally distributed than work income; and (2) because of the progressive nature of government benefits, countries with stronger public income security programmes are better able to reduce income inequalities during old age. The analysis is performed by comparing age groups within seven OECD countries (Canada, Germany, the Netherlands, Norway, Sweden, the United Kingdom, and the United States of America) using Luxembourg Income Study data from around 2000. Both hypotheses are supported. Several conclusions are drawn from the findings.

This paper presents the findings of a survey of the current Dynamic Financial Analysis (DFA)/Financial Condition Report (FCR) practices in the United Kingdom general insurance industry. An independent samples t test for non-respondent bias was conducted, and the results suggest that the respondent sample is representative of the survey population. The survey results revealed: (1) that the use of DFA techniques in the industry was limited; (2) that scenario testing was the most frequently used technique; (3) that the most common DFA application was the evaluation of reinsurance programmes; (4) that less than ten scenarios were run regularly; (5) that inflation was the most frequently modelled economic variable; (6) that the capability of asset modelling of general insurers was restricted; (7) that the most common method of liability modelling was to use all in force policies in aggregate; (8) that the most common projection periods in DFA and business planning were three years; (9) that the main reason for not using DFA techniques and producing FCR was lack of need; and (10) that views on whether a Guidance Note on FCR specifically for general insurers should be introduced differed.

Mutations in the BRCA1 and BRCA2 genes confer very high risk of breast cancer (BC), but only account for about 25% of the observed familial clustering of BC. Antoniou et al. (2002) proposed a model which included the BRCA1 and BRCA2 genes, and a polygenic component which acted multiplicatively on the rate of onset of BC. We use this model to find premium rates for critical illness insurance: (a) given knowledge of an applicant's polygenotype; and (b) given knowledge of a family history of BC or ovarian cancer. We find that the polygenic component causes large variation in premium rates even among non-mutation carriers, therefore affecting the whole population. In some cases the polygenic contribution is protective enough to reduce or remove the additional risk of a BRCA1/2 mutation, leading to cases where it will be advantageous to disclose genetic test results which are adverse in absolute terms. Premiums based on family history are lower than those found in an earlier study which attributed all genetic BC risk to the BRCA1/2 genes.

Structural instability in economic time series is widely reported in the literature. It is most prevalent in such series as price indices and inflation related data. Many methods have been developed for analysing and modelling structural changes in a univariate time series model. However, most of them assume that the data are generated by one fixed type (linear or non-linear) of the time series processes. This paper proposes a strategy for modelling different segments of an economic time series by different linear or non-linear models. A graphical procedure is suggested for detecting the model change points. The proposed procedure is illustrated by modelling annual United Kingdom price inflation series over the period 1265 to 2005. Stochastic modelling of inflation rates is an important topic to actuaries for dealing with long-term index linked insurance business. The proposed method suggests dividing the U.K. inflation series into four segments for modelling. Inflation projections based on the latest segment of the data are obtained through simulations. To get a better understanding of the impact of structural changes on inflation projections we also perform a forecasting study.

In this paper we address the problem of valuing (corporate) pension plans, and in particular defined contribution based pension plans. Several pension plans are proposed, both with and without rate of return guarantees. Both maturity and annual guarantees are considered. Emphasis is also given to the risk management of pension plans.

To tie the analysis closer to real-world problems, we allow for both periodic premium and pension payments and mortality risk to be taken into account. Some new results on forward-start guarantees are also derived.

This paper investigates the use of censored regression quantiles in the analysis of claim termination rates for income protection (IP) insurance. The paper demonstrates the importance of modeling quantiles given the growing interest of regulators and others in stochastic approaches to valuation of insurance liabilities and risk margins.

To gain insight into the use of Dynamic Solvency Testing (DST) and Financial Condition Reporting (FCR), a questionnaire was distributed to Appointed Actuaries in United Kingdom life offices. The response rate of the main survey was 76%. An independent-samples t-test for non-respondent bias was conducted and the results suggest that the respondent sample is representative of the survey population. Results from the 62 firms responding revealed: (1) Scenario testing was the most commonly used DST techniques. (2) Most life offices regularly run less than ten scenarios in scenario testing. (3) Most life offices reported using a five-year forecast period in DST. (4) The two most commonly seen difficulties are: difficulties in communicating complex issues to non-specialists, and how to present extremely adverse scenarios without causing undue concern. (5) Nearly all life offices use FCR. (6) Guidance Note 2 is generally considered acceptable. (7) Compared with the results reported by previous studies, the use of DST techniques is now more common in life offices. (8) There is a significant difference in DST/FCR practices between with-profits and non-profit offices.

Almost all over the world, decreasing mortality rates and increasing life expectancy have led to greater interest in estimating and predicting mortality. Here we describe some of the pitfalls which can result from the use of the standardised mortality ratio (SMR) while evaluating the development of mortality over time, in particular when SMRs are applied to insurance portfolios varying dramatically over time. Although an excellent comparative study of a single-figure index for a number of countries was recently done by Macdonald et al. (1998), we advocate care when attempting to extend this type of method to insurance data. Here we promote the use of genuine multiplicative modelling such as in Felipe et al. (2001), who compared the mortality rates in Denmark and Spain. The starting point for our study was the two-dimensional mortality estimator of Nielsen & Linton (1995), which considers mortality as a function of chronological time and age. From the principle of marginal integration (see Nielsen & Linton, 1995, and Linton et al., 2003), estimators of the multiplicative model can be obtained from this two-dimensional estimator. An application of the method is provided for mortality data of the United States of America, England & Wales, France, Italy, Japan and Russia.