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.

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.

It is well known that the number of the physical sciences is continually increasing, by a process of development from within. We constantly see divisions and branches of existing sciences cultivated and developed until they acquire a separate existence as new and independent sciences. For it has long been impossible for a single person to master the whole, or even a considerable part of these sciences, and the necessity for a division of labour is continually becoming more and more felt here, as elsewhere. It is, however, comparatively seldom that the number of the sciences is increased by the addition to them of an entirely new one, and therefore the case of which I am about to speak appears to deserve our particular attention. For I shall presently prove that a department of science, which has not hitherto belonged to the physical sciences, is now being so developed and perfected, that in a very short time it will claim admission into the number on equal terms with the others. This department of science is Statistics. The science of Statistics in its present form has now existed a full century. It owed its birth, as well as its name, to Achenwall of Göttingen, about the middle of the last century.

Pension fund is created for what it will do while in full operation—not for what will emerge when it is wound up nor for what it might provide for members during their employment. Nevertheless, the dissolution provisions are important: they may reflect the philosophy on which, or the limitations within which, the fund is financed but it is of paramount importance that they should make llowance for the considerable problems that can and do arise on a dissolution acutally taking place.

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 paper seeks to examine the fundamental principles underlying the periodic actuarial investigations of life insurance companies. It attempts to define the attributes of an equitable and efficient set of standards, to classify the causes of failure of life offices and to enumerate the realities of any life office. Having examined the background to the present situation it then proceeds to attempt to derive a general valuation standard.

This paper has the strictly practical objective of devising procedures for managing Equity portfolios to the best advantage.

First, Modern Portfolio Theory, (MPT) which has been developed over the last 35 years with just this objective, is critically examined; from a study of the history of MPT and of its philosophy, principles and practices, the authors conclude that this discipline makes no contribution whatever to improving the performance.

The Index Fund step-up is a sterile concept. Surely a professional investment manager, using modern techniques of data banks, investment analysis, etc. should improve on the Index performance. This objective is in conflict with the Perfect Market Principle. For the less erudite investors, who are, of course, in the majority, the Perfect Market Principle may well apply, at any rate, to the well researched leading shares. However, the Perfect Market Principle should not apply to the erudite, professional investor, well equipped and well advised, who should be able to find many opportunities for situations with undervalued and overvalued shares, both among the leading issues and particularly within the smaller companies that get less research attention.

In the current financial climate takeovers of proprietary life companies by other life companies, amalgamations of mutuals and demutualisations have become more and more prevalent. However in respect of takeovers, the process does not end with the purchase, but normally results in the transfer of the long-term business of one of the companies to the other. To optimise synergy and administrative efficiency, there may be a need to reconstruct the amalgamated funds.

The author has been involved as Appointed Actuary and internal project manager in such transfers of business within proprietary companies and has also acted as an independent actuary and as an external project manager for other transfers. One of these transfers involved four companies transacting both with-profits and unit-linked business in which the interests of both policyholders and shareholder had to be protected. He considered this transfer to be of sufficient interest to merit the preparation of a paper discussing the issues which arose. Although the paper is principally based on that transfer as a case study, relevant and related factors arising in other transfers have been included where appropriate, as have references to the role of the actuary before, during and after reconstruction.

In the case study, the scheme of transfer and the associated reconstruction of corporate structure involved merging three separate with-profits funds, merging many unit-linked funds (including unitised with-profits) and, subject to appropriate compensation, rationalisation of the rights to surplus attributable to both with-profits policyholders and shareholder.

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 (re)insurance industry is faced with a growing risk related to the development of information technology (IT). This growth is creating an increasingly digitally interconnected world with more and more dependence being placed on IT systems to manage processes. This is generating opportunities for new insurance products and coverages to directly address the risks that companies face. However, it is also changing the risk landscape of existing classes of business within non-life insurance where there is inherent risk of loss as a result of IT events that cannot be or have not been excluded in policy wordings or are changing the risk profile of traditional risks. This risk of losses to non-cyber classes of business resulting from cyber as a peril that has not been intentionally included (often by not clearly excluding it) is defined as non-affirmative cyber risk, and the level of understanding of this issue and the cyber peril exposure from non-cyber policies varies across the market. In contract wordings, the market has remained relatively “silent” across most lines of business about potential losses resulting from IT-related events, either by not addressing the potential issue or excluding via exclusions. Some classes of business recognise the exposure by use of write-backs. Depending on the line of business, the approach will vary as to how best to turn any “silent” exposure into a known quantity either by robust exclusionary language, pricing or exposure monitoring. This paper proposes a framework to help insurance companies address the issue of non-affirmative cyber risk across their portfolios. Whilst the framework is not intended to be an all-encompassing solution to the issue, it has been developed to help those tasked with addressing the issue to be able to perform a structured analysis of the issue. Each company’s analysis will need to tailor the basis of the framework to fit their structure and underwriting procedures. Ultimately, the framework should be used to help analysts engage with management on this issue so that the risk is understood, and any risk mitigation actions can be taken if required. In the appendix, we present a worked example to illustrate how companies could implement the framework. The example is entirely fictional, is focused on non-life specialty insurance, and is intended only to help demonstrate one possible way in which to apply the framework.