In most branches of mathematics, the actual use of fundamental processes in the form which the first definitions suggest, is often supplanted, either by processes of greater skill, or by the use of pure reasoning. In the subject of which this paper treats, there has not been much attempt to connect formulæ by reasoning. The actual exhibition of successive annual results has been the only method extensively employed; and it throws the required total result into a series of terms: this series is either algebraically summed, or calculated term by term for insertion in a table.

The present paper is intended to show that this summation of algebraical series may be dispensed with, at least in questions of annuities certain : and also that common points of principle, which the ordinary methods leave altogether out of sight, will reduce many questions of life annuities to an absolute coincidence of form with the corresponding questions of ordinary annuities.

Staple Inn and the Patent Office are only separated by the width of a garden, and it might be wondered why none of the many ingenious schemes of insurance has ever been protected by patenting it. Such protection of an idea should be impossible, as will be explained later, but in 1778 one John Knox ‘Of Richmond in the County of Surry, Gentleman’ took the first step towards such a patent by petitioning King George III ‘that with great assiduity, art and pains and after many laborious calculations and at a considerable expence’ he had invented ‘A Plan, Different to any before that Time Discovered, for Assurance on Lives from Ten to Eighty Years of Age, upon a Twofold Beneficial Principle, Making a certain provision as well for Subscribers or their Representatives upon the Death of the Person on whose Life Assurance should be made within the Term Assured for, as also by Means of a Reserved Capital for the Surviving Subscribers whose Nominees should be Living at the Expiration of such Term….’

It is probable that some of the points I venture to bring forward have already suggested themselves to other students, but in view of the interest at present attaching to selection, it seems an opportune time for putting forward any considerations that may help to throw light on a somewhat complicated subject.

Questions of combination are so connected with an actuary's business, that no apology is necessary for offering solutions to the notice of the readers of this Journal.

When two systems, A and B, of combinations, each having its own individual cases, are so related that each case of A admits of being converted into a case of B, and into one only, by a rule which will not convert any other case of A into that same case of B, it may be said that the system A is convertibly within B. It is obvious that if A be convertibly within B, and B convertibly within A, the numbers of cases in the systems A and B are equal.

It is stated in the notes to Cousin's éloge, and has been repeated, that Fourier was placed at the head of a bureau de statistique by the prefect of the Seine, the Comte de Chabrol. But there is hardly any authentication. Anything done in the subject by Joseph Fourier, the most powerful working member of the Egyptian commission, the originator of mathematical results of the first order of genius, novelty, and utility, and an experienced public man, must be worthy of attention. But so little is his statistical career known, that the Biographie Universelle (Michaud, 1856) only ventures its mention of the connexion of Fourier with the volumes presently described as suivant plusieurs personnes bien instruits.

This paper looks at the reasons why a UK life insurance company would wish to consider expanding into an overseas market, the factors it ought to bear in mind when deciding upon which country or countries to enter and the entry routes open to a company wishing to expand overseas.

By way of examples of overseas life insurance markets, the paper provides a detailed description of the German and Indian life insurance markets.

The text of these papers, together with the abstract of the discussion held by the Faculty of Actuaries on 15 March 2004, are printed in British Actuarial Journal, 10, IV, 685-898.

The UK defined benefit pension scheme landscape has changed dramatically over the last few decades. During this period of change, conflicting views regarding the measurement of both assets and liabilities has made communication challenging. In turn, this has led to an under appreciation of risk and often suboptimal decision making. This paper seeks to draw together a variety of contrasting views to provide a coherent framework for stakeholders to meet pension scheme obligations over time.

The proposed framework encourages agreement between both scheme sponsors and trustees towards a common target through a well articulated plan or “flight path”. In addition, the proposed flight path structure provides a common basis underpinning the measurement of both pension obligations and the risks inherent in any plan to meet those obligations.

Some UK insurers have been using real-world economic scenarios for more than 30 years. Popular approaches have included random walks, time series models, arbitrage-free models with added risk premiums or 1-year Value at Risk distribution fits. Based on interviews with experienced practitioners as well as historical documents and meeting minutes, this paper traces historical model evolution in the United Kingdom and abroad. We examine the possible catalysts for changes in modelling practice with a particular emphasis on regulatory and socio-cultural influences. We apply past lessons to provide some guidance to the direction of capital market modelling in future, which has been key for business and strategy decisions.

The text of this paper, together with the abstract of the discussion held by the Institute of Actuaries on 25 October 1999, are printed in British Actuarial Journal, 6, I, 55-141.

However, when this paper was discussed by the Faculty of Actuaries, the following ‘Survey of Practice’ had been carried out, and was also presented.

This paper explores dependencies between operational risks and between operational risks and other risks such as market, credit and insurance risk. The paper starts by setting the regulatory context and then goes into practical aspects of operational risk dependencies. Next, methods of modelling operational risk dependencies are considered with a simulation study exploring the sensitivity of diversification benefits arising from dependency models. The following two sections consider how correlation assumptions may be set, highlighting some generic dependencies between operational risks and with non-operational risks to assist in the assessment of dependencies and correlation assumptions. Supplementary appendices provide further detail on generic dependencies as well as a case study of how business models can lead to operational risks interacting with other risks. Finally, the paper finishes with a literature review of operational risk dependency papers including correlation studies and benchmark reports.