Some years ago I had the privilege of reading a paper on Contingent Reversions, &c., before this Institute, and the proposals I then made for the treatment of the premiums on the insurances to be set up in connection with reversionary transactions were received with general condemnation, nor have they since, so far as I know, met with any practical support, although I have seen no reason to alter my opinion of the soundness and practicability of the views I then put forward. I am not afraid on this occasion of meeting with like opposition, as the methods I am now going to deal with have been carried into practice already by the Society with which I am connected, and by way of reassurance, if not otherwise, have examples on the books of many of the life offices, both in England and Scotland.

In the first part of the paper the general nature of the problem is dealt with in relation to the movements which take place in group pension schemes and the information which is readily available from the normal office records. The choice of valuation date is discussed and some of the differences which exist between private funds and office schemes and which lead to essentially different treatment are noted.

The valuation of schemes providing future service pension by the single and annual premium methods is discussed separately, each being developed from a consideration of the simplest form of contract to the more elaborate forms, and approached from the standpoint of the net premium and gross premium methods of valuation. Under each heading theoretical formulas are given and these are considered from the practical standpoint of designing accurate valuation methods and of devising, without appreciable loss of accuracy, approximate methods which reduce considerably the arithmetical work. Throughout, the effort is made to reduce the data to be recorded to a minimum and to use, wherever possible, the data which an office will require for its costing purposes.

The paper includes a section on past service pension in which is given a theoretical review of the various methods commonly used to provide pensions.

In the appendices it is demonstrated how Trachtenberg's formula may be adapted for valuation of a single premium scheme by the net premium approach and an example is given of the working of the suggested short method in the valuation of an actual scheme together with a valuation “in extenso” for comparison of the results obtained.

In a paper by the late Mr. Samuel Brown “On the Rate of Mortality and Marriage among Europeans in India” (J.I.A., xi, 1), reference is made to a method used by Griffith Davies to deduce rates of mortality from the records of the Madras Military Fund. It appears that Davies ascertained the average age of the lives in each of certain groups into which the experience naturally divided itself, and obtained the ratios which the actual deaths in the several groups bore to the corresponding number expected according to the Northampton Table at the average age. These ratios were then set out as ordinates corresponding to abscissae representing years of age, and a continuous curve was drawn in the usual way, by reading off which the graduated ratios for each age were obtained, and from these the graduated rates of mortality were at once formed.

Older people are higher contributors to mortality excess and most sensitive to environmental influences, e.g. temperature. As the population ages, variability in temperature is liable to impact a large proportion of life insurance or pension policies in a portfolio. Climate change is projected to significantly affect future mean temperatures. Moreover, future changes in mean temperature are estimated to vary across different regions of the United Kingdom. Accordingly, the present paper investigates the potential impact of future mean temperature changes on older-age mortality in England & Wales and Scotland. The corresponding effect on older-age mortality differences between England & Wales and Scotland is also investigated.

This paper seeks to establish good practice in setting inputs for operational risk models for banks, insurers and other financial service firms. It reviews Basel, Solvency II and other regulatory requirements as well as publicly available literature on operational risk modelling. It recommends a combination of historic loss data and scenario analysis for modelling of individual risks, setting out issues with these data, and outlining good practice for loss data collection and scenario analysis. It recommends the use of expert judgement for setting correlations, and addresses information requirements for risk mitigation allowances and capital allocation, before briefly covering Bayesian network methods for modelling operational risks.

The corporate landscape of United Kingdom financial services has changed considerably in the last fifteen years with virtually all the main players now shareholder-owned. The dominance of shareholder ownership may not last for ever and the pendulum could swing back to alternate structures. Should the actuarial profession look ahead and consider what, if anything, could be done to encourage diversity? This paper considers some of the issues involved and raises some questions for the profession to discuss.

In adventuring upon a Second Presidential Address, the energy of hope and freshness which stimulated me in the former effort have vanished into trepidation of feeling. For I am unhappily conscious that I then exhausted any meagre resources I possessed of novel presentation of thought and research, and was reduced to virtual bankruptcy of serviceable suggestiveness which the interval of time has failed to annul.

In treating of the above subject, it cannot be expected that any new principles will be put forward, or that any great amount of novelty will be found in the method of handling the question. All that I have aimed at is, to apply acknowledged principles to the discussion of a question of considerable practical interest at all times, and more peculiarly so at the present time.

This paper reviews the market structure of the U.K. with-profits life insurance market and the potential effect on how life insurers operate. We consider the competitiveness of the market, quantifying the increase in the degree of concentration since 2000, and establishing that inherited estates may offer some protection from competition for incumbent firms. However, there is a significant degree of mobility in market positions of leading firms. Analysis of costs indicates some large differences between firms, with larger firms experiencing lower cost ratios, indicative of economies of scale. There are some marked differences in insurers' prices, the data showing that charges tend to be lower on unit-linked than on with-profits policies. The paper suggests that while there are potential concerns about how the market operates for consumers, the impact is limited by the dramatic reduction in new with-profits business.

ALL the methods of group valuation submitted to the Institute in the last decade require the calculation of the second sum of the quantities valued, whether in the form of multiplications by —4½, —3½, … 3½, 4½, i.e., the second sum about the centre, or the more convenient second sum about the end. The object of this paper is to show that the α, β method can be transformed so as to avoid this difficulty.