Notwithstanding the very large amount of leasehold property, which in the course of every year is bought and sold in this country, and notwithstanding the extensive transactions—of almost hourly occurrence—in the public market, in Government and other temporary Annuities, the subject of the rate of interest which any given purchase will yield the buyer is very imperfectly understood, even by those most deeply interested in the inquiry, unless they happen to be at the same time well versed in actuarial computations.

This paper describes how to calculate approximate prices of options if investment markets are being modelled according to the Wilkie investment model.

The investigation of the experience, and valuation of the liabilities, of what are known as Clerks' Associations, present some features of special interest; and I have thought that it might he useful to discuss and explain some of the methods that have been employed in analyzing the data, and in deducing therefrom the tables of money values appropriate for the valuation of the risks.

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.

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.

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.

The theory surrounding sickness rates has received little attention in the United Kingdom during the past two decades. This may be a consequence of the assumption by the British Government of the role of principal insurer against sickness, and the resulting reduction in numbers of those who otherwise might have turned to the traditional friendly society for sickness insurance. It is unfortunate that the decline in interest in sickness rates should have coincided with the burgeoning of the theory of stochastic processes, for sickness is a stochastic process.