In this paper we present an approach to the graduation of select mortality data and we illustrate this approach by graduating the CMIB's data for Female Permanent Assurances 1979–1982. The difference between our approach and that of the CMIB is that we graduate simultaneously by attained age and duration since selection.

The Calculus of Differences is a somewhat extensive subject, but it is not necessary now to go far into it, or to occupy ourselves with its application to other than the simplest class of functions, namely, rational, algebraical, and integer functions. The theorems we require might have been left to be deduced as occasion for them should arise; but it has been thought better— and the arrangement will certainly be more convenient for reference—to bring the greater portion of them together in this place.

A great deal of theoretical and empirical work has been carried out in recent years, particularly in the United States, on the use of mathematical models as an aid to the selection of investment portfolios containing equities. The present paper attempts to survey some of the more important advances that have been made, and to assess them in relation to the problems that managers face in the running of a portfolio.

Although this paper deals with the application of mathematical formulae to mortality data, it is not concerned with ‘graduation’ if that word is held to imply the fitting of a particular curve to a particular experience with the object of satisfying statistical tests. Nor is the paper concerned with the development of any philosophical theory of mortality. The experiments which it describes were undertaken in the hope of finding a standard type of curve which would give a good over-all representation of adult mortality in general. If such a curve could be found, an examination of the variations in its parameters might contribute something to an understanding, not of the nature of mortality itself, but of the differences—more particularly the secular differences—between one mortality experience and another.

Perhaps the most important lesson many of you can learn—one that is frequently lost sight of by persons who are solely or mainly engaged in theoretical studies—is that the researches which you are pursuing, by the aid of a variety of complicated symbols, are, after all, not merely elaborate mathematical puzzles to be solved principally for the purpose of awakening or sharpening the intellect, but have, for you at least, an eminently practical aim as well, and are insisted on as part of the education of an Actuary, with a view to their serving as the framework on which, when afterwards called upon, he must be prepared to base actual business transactions involving large sums of money, or, it may be, to lay down principles for the regulation in all its various details of a life assurance office.

The state of the law in respect to Joint-Stock Companies, and associations for business purposes generally, remained in the same unsatisfactory condition which I have described in the previous section down to this time. Those great Insurance Associations, with millions of capital subscribed, in many cases, by the merchant princes of the land, for purposes admittedly the most beneficent, were simple partnerships, almost without legal recognition, except for purposes tending to their detriment or destruction. They could be attacked or pulled down by legal process readily enough; but they could only protect themselves against fraud, or recover their just debts by the most cumbersome of processes. What they had a right to expect, as institutions designed to aid largely in the accumulation of national wealth, was protection in carrying out their laudable designs; but of this they had not a vestige. Not only was every holder of stock in a proprietary company primarily and personally liable to his last shilling for the engagements of the partnership, but every policy-holder in a mutual society, being a member of, and therefore a partner in such society, was equally liable for all its engagements.

J.I.A. Vol. LXVII, Part I. Page 13, line 18.

For “T.F.A. Vol. XIII, p. 149”

read “T.F.A. Vol. XIII, p. 419”.

This abstract relates to the following paper: IFoA/LLMA (2014) Longevity Basis Risk. A methodology for assessing basis risk by Cass Business School and Hymans Robertson LLP. Available at http://www.actuaries.org.uk/sites/all/files/IFoA%20LLMA%20Longevity%20Basis%20Risk%20Report_0.pdf

Operational Risk is one of the most difficult risks to model. It is a large and diverse category covering anything from cyber losses to mis-selling fines; and from processing errors to HR issues. Data is usually lacking, particularly for low frequency, high impact losses, and consequently there can be a heavy reliance on expert judgement. This paper seeks to help actuaries and other risk professionals tasked with the challenge of validating models of operational risks. It covers the loss distribution and scenario-based approaches most commonly used to model operational risks, as well as Bayesian Networks. It aims to give a comprehensive yet practical guide to how one may validate each of these and provide assurance that the model is appropriate for a firm’s operational risk profile.