1.1 There are three starting points for this paper. The first is Marshall Field's challenging Presidential Address to the Institute of Actuaries in 1986 on the subject of ‘Risk and Expectation’. The second is the example, still fresh in our minds, of a medium-sized mutual life office which overstretched itself and found it necessary to merge with a competitor. The third is the impending requirement, stemming from the Financial Services Act 1986, to give an investment client, including the holder or prospective holder of an insurance savings contract, what is described as ‘best advice’.

This paper develops the Daykin et al (1994) asset/liability model to examine specifically the effects of different reinsurance programmes on the capital of a direct insurance company. By modelling the gross premiums and claims separately from the impact of reinsurance on them, it is possible to examine directly the effects of different reinsurance programmes on a company's expected performance just as easily as changes in asset mix or business volumes. The paper goes on to discuss the necessary assumptions to be built into such a model, and then gives a worked example. The emphasis of the paper is on management reporting rather than on mathematical detail.

So much has been written on the algebra of formulæ for graduating an irregular series by means of successive summations, and on the theoretical errors introduced by this process, that there is possibly some danger of the underlying principles, on which all such formulæ are founded, being overlooked or insufficiently understood. In the present note an attempt is made to deal with this matter from first principles, with the object of rendering clear how such formulæ Work and why it is that they produce, with greater or less success according to the nature of the particular formula, a smooth succession of values from rough and irregular data.

The Transactions of the Royal Society contain the first Life Table. It was constructed by Halley, who discovered its remarkable properties, and illustrated some of its applications. The Breslau observations did not supply Halley with the data to frame an accurate table, for reasons which will be immediately apparent; but the conception is full of ingenuity, and the form is one of the great inventions which adorn the annals of the Royal Society.

Demographic and societal changes make it more and more indispensable to protect against the risk of care costs surpassing a person’s financial means. Nevertheless, only few governments have acted to create public funding systems that, if existent at all, usually only cover part of the expenses for elder care. Long-term care insurance (LTCI) is designed to fund basic care needs in later life, such as washing and dressing. Regardless of where individuals receive this support in old age, how it is funded is a growing issue. In many countries, people may augment their compulsory state system with private policies available from insurance companies.

In Germany, a well-established public system that underwent major reforms exists. From 2017 onwards, a completely new care definition and assessment process replaced the former ones. Two major changes constitute the reform: First, when evaluating the need for care, the former focus on estimating the length of time required for care was replaced by the determination of the degree of independence. Second, cognitive impairments will be acknowledged more adequately than in the past, where the focus was on physical abilities. Furthermore, the contribution to be paid by the care recipient in a nursing home will no longer be dependent on the severity of the care need.

In Germany, private LTC products used a combination of the social security definition, an ADL-based trigger and a dementia trigger until the end of 2016. Thus, the reform has repercussions for the local private insurance industry. What would happen to in-force business, how a new benefit trigger should look like, how old and new definition compare and how pricing rates can be derived were only some of the questions that had to be answered in advance.

The reform could point the way for future public schemes and private policies elsewhere. Which questions had to be answered and what issues had to be solved in advance, together with lessons learned during and shortly after the reform was undertaken, can serve as an accompaniment for the introduction or reform of public LTC schemes and for the local insurance industry in other countries.

The paper comments on the estimation and sensitivity of the retail price inflation component of the stochastic financial model proposed by Professor Wilkie. Statistical tests provide evidence of nonindependence and non-normality of residuals, suggesting non-linearity. However, it is noted that the model is most sensitive to the assumption of long-term mean inflation.

It is not proposed in the present paper to take up any original investigation, the main object being to bring up to date the papers submitted to the Institute in 1876 and 1877, and which appeared in J.I.A., xix, p. 381, and xx, p. 233. These papers were written not very long after the publication of the Twenty Offices' Experience, with the Monetary Tables based thereon, and to it they were almost entirely devoted. The peculiar rates of mortality prevailing amongst assured lives were investigated, by means of ten mortality tables calculated for central ages at entry, tables which were called by name “Analyzed.” That name has since been superseded by the name “Select”, and the tables themselves, together with the annuity tables based upon them, have become obsolete, their place having been taken by Dr. Sprague's much more complete, and much better, “Select” Tables. The Analyzed Mortality Tables, however, served their purpose, as the main object in taking the matter up was, to estimate the reserves of life offices when the mortality of lives assured is kept separate according to age at entry.

This paper describes how the system of life office taxation in the U.K. impinges on the amount and the emergence of life assurance business profit. It considers how to allow for taxation in the assessment of product profitability and company valuation. Finally, the paper provides a brief overview of the methods of taxation of alternative savings products and of tax systems in the European Community, with a view to drawing conclusions as to possible future changes to the framework of life taxation in the U.K.

This paper argues that all reserving methods based on claims triangulations (the “triangle trick”), no matter how sophisticated the subsequent processing of the information contained in the triangle is, are inherently inadequate to accurately model the distribution of reserves, although they may be good enough to produce a point estimate of such reserves. The reason is that the triangle representation involves the compression (and ultimately the loss) of crucial information about the individual losses, which comes back to haunt us when we try to extract detailed information on the distribution of incurred but not reported (IBNR) and reported but not settled (RBNS) losses.

This paper then argues that in order to avoid such loss of information it is necessary to adopt an approach which is similar to that used in pricing, where a separate frequency and severity model are developed and then combined by Monte Carlo simulation or other numerical techniques to produce the aggregate loss distribution.

A specific implementation of this approach is described, whose core feature is a method to produce a frequency model for the incurred but not reported claim count based on the empirical distribution of delays (delay = the time between loss date and reporting date), after adjustments to make up for the bias towards smaller delays. The method also produces a kernel severity model for the individual losses, from which the severity distribution of each year of occurrence can be derived. By combining the frequency and severity model in the usual way (e.g. through Monte Carlo simulation), an aggregate model for IBNR and UPR losses can be produced.

As for RBNS losses, we suggest using one of the many methods to analyse the distribution of IBNER (incurred but not enough reserved) factors to produce a possible distribution of outcomes.

A case study based on real-world liability claims is used to illustrate how the method works in practice.

Also, in a first step towards validating the method for calculating IBNR and comparing it with existing methods, a series of experiments with artificial data sets was undertaken, which show a drastic reduction in the prediction error of both the IBNR claim count and the IBNR total amount with respect to the standard chain ladder method. And what is perhaps most promising, the experiments show that the distribution of IBNR reserves is much closer (in terms of the Kolmogorov-Smirnov distance) to the “true” one than that based on Mack's method in the way it is normally applied. The method promises therefore a more accurate assessment of the uncertainty around reserves.

The Mathematical Theory of Probability has, as is well known, two main branches:

1°. Direct or Deductive Probability, in which the behaviour of a system is deduced from a knowledge of its constitution.

Thus the problem “What is the probability of throwing a double-six in a single cast of two dice” belongs to deductive probability, since we know the constitution of the dice–that they are symmetrical six-sided bodies–and from this knowledge we deduce the probability of a double-six.

And 2°. Inverse or Inductive Probability, in which the constitution of a system is inferred from its observed behaviour.

As an example of Inductive Probability, suppose we visit a rifle-range and find a man firing at the target. At first we know nothing regarding his skill as a marksman ; but after watching a few shots we are able to form a rough estimate of it, and this estimate becomes more sharply defined and more confident the longer we observe his performance , so that ultimately we attain to a trustworthy knowledge of his “constitution” as a marksman, i.e. we can assign the probability that his next shot will hit or miss.

1.1. This paper explores the possibility that a company which sells unit-linked policies with death and maturity benefit guarantees may follow an investment strategy which reduces the risks associated with them. It originated when the author was requested by the Institute to study papers on the subject by P. P. Boyle, M. J. Brennan and E. S. Schwartz of the University of British Columbia in Canada and also a paper presented to the Society of Actuaries in Ireland by J. C. Fagan.

Life Assurance is an institution possessing such an important influence in the welfare and well-being of Society that it is most essential the principles upon which it is based and conducted should be such as to ensure its lasting stability and prosperity.

After a Life Assurance Office has been once established upon a firm basis, there is no part of its management so important as that relating to the periodical valuation of the liabilities under its policies. It is my object in this essay to inquire into the various methods adopted for that purpose in the present day; and to consider the various results they produce when different tables of mortality and rates of interest are employed in the calculations; and also to ascertain the effects which the employment of different data may have upon the present and future condition of an Office.

The origin and progress of the principles of insurance are subjects, which not only call for the endeavour to elicit and clear from seeming contradictions such records of the insurer’s calling as are blended with the remote history of mercantile customs and laws, but which likewise particularly suggest the necessity of some essay to connect those rude outlines with the more advanced stage of the theory, in its immediate alliance with the sciences of applied probabilities and political or social arithmetic.

1.1.1. In the course of the discussion of the paper by Praetz at the International Congress of Actuaries in Sydney, reference was made to the existence of the ongoing Expense Investigation conducted amongst life offices in the United Kingdom. Considerable interest was aroused and it was subsequently suggested that a paper describing this investigation be presented to the actuarial bodies in order that data on life office costs might be made available to the profession and its significance discussed. In agreeing to present such a paper the authors considered that its scope should be extended to include a study of the attitudes of offices and actuaries to expense analysis and control and of the uses made by offices and actuaries of the results of the Expense Investigation and other expense analyses.

The asset allocation is a crucial decision for pension funds, and this paper analyses the economic factors which determine this choice. The analysis proceeds on the basis that, in the absence of taxation, risk sharing and default insurance, the asset allocation between equities and bonds is indeterminate and governed by the risk/return preferences of the trustees and the employer. If the employing company and its shareholders are subject to taxation, there is a tax advantage in a largely bond allocation. Risk sharing between the employer and the employees often means that one group favours a high equity allocation, while the other favours a low equity allocation. Underpriced default insurance creates an incentive for a high equity allocation. When taxation, risk sharing and underpriced default insurance are all present, it is concluded that the appropriate asset allocation varies with the circumstances of the scheme; but that a high equity allocation is probably inappropriate for many private sector pension schemes.

In the train of the economic integration of Europe, a lively discussion has, for some time, been carried on about appropriate criteria of solvency for insurance undertakings in respect of life and non-life assurance. The conflict over the proposals for solvency requirements in non-life assurance still occupies the foreground. Here it is the proposed directive put up for discussion by the E.E.C. authorities which is of particular importance. This directive puts forward quantitative conditions for the solvency reserves of companies carrying on non-life business.