The paper traces the history of the development of a with-profit system for a specialist unit-linked office. The marketing problem, to which this was the chosen solution, is discussed and a number of possible future developments are then considered. The second half of the paper is devoted to discussion of the question of matching assets and liabilities for the range of products developed. Although the paper deals with developments in a particular office the authors' intention is to provide a different perspective on the problems associated with conventional with-profit business which will be of more general interest.

Cyber Operational Risk: Cyber risk is routinely cited as one of the most important sources of operational risks facing organisations today, in various publications and surveys. Further, in recent years, cyber risk has entered the public conscience through highly publicised events involving affected UK organisations such as TalkTalk, Morrisons and the NHS. Regulators and legislators are increasing their focus on this topic, with General Data Protection Regulation (“GDPR”) a notable example of this. Risk actuaries and other risk management professionals at insurance companies therefore need to have a robust assessment of the potential losses stemming from cyber risk that their organisations may face. They should be able to do this as part of an overall risk management framework and be able to demonstrate this to stakeholders such as regulators and shareholders. Given that cyber risks are still very much new territory for insurers and there is no commonly accepted practice, this paper describes a proposed framework in which to perform such an assessment. As part of this, we leverage two existing frameworks – the Chief Risk Officer (“CRO”) Forum cyber incident taxonomy, and the National Institute of Standards and Technology (“NIST”) framework – to describe the taxonomy of a cyber incident, and the relevant cyber security and risk mitigation items for the incident in question, respectively.Summary of Results: Three detailed scenarios have been investigated by the working party:

• ∙ Employee leaks data at a general (non-life) insurer: Internal attack through social engineering, causing large compensation costs and regulatory fines, driving a 1 in 200 loss of £210.5m (c. 2% of annual revenue).

• ∙ Cyber extortion at a life insurer: External attack through social engineering, causing large business interruption and reputational damage, driving a 1 in 200 loss of £179.5m (c. 6% of annual revenue).

• ∙ Motor insurer telematics device hack: External attack through software vulnerabilities, causing large remediation / device replacement costs, driving a 1 in 200 loss of £70.0m (c. 18% of annual revenue).

• ∙ While the presented scenarios are deemed material at this point in time, the threat landscape moves fast and could render specific narratives and calibrations obsolete within a short-time frame.

• ∙ There is a lack of historical data to base certain scenarios on and therefore a high level of subjectivity is used to calibrate them.

• ∙ No attempt has been made to make an allowance for seasonality of renewals (a cyber event coinciding with peak renewal season could exacerbate cost impacts)

• ∙ No consideration has been given to the impact of the event on the share price of the company.

• ∙ Correlation with other risk types has not been explicitly considered.

The paper is largely concerned with discussing what is a suitable valuation basis for deciding the rate of bonus an office should declare if it wishes to maintain this rate of bonus in the future as long as conditions remain reasonably stable.

Because of recent developments, such as the substantial proportion of the assets now held in ordinary shares, the reverse yield gap, the present historically high rate of interest and the growth of immediate annuity and other single premium business, a net premium valuation in conjunction with assets at balance sheet values gives an inadequate view of the position of an office. With the advent of electronic computers a more realistic and comprehensive view is now possible, and the paper advocates a valuation of the liabilities on a modified bonus reserve basis with rates of interest and bonus the same as those implicit in the current premium rates, and a valuation of the assets at a notional rate of interest equal to the rate used in the valuation of the liabilities. The various problems arising in the valuation of assets, and especially of ordinary shares, at a notional rate of interest are discussed, and also the adjustments necessary if the assets and liabilities are not fully matched.

The final decision on the rate of bonus to be declared must in the end be a matter of judgment, as it depends on many factors which cannot be accurately forecast, such as the future course of the rate of interest, the amount of new business and the rates of premium charged. Nevertheless, it is now possible to make this decision in the light of a very much fuller analysis of the position than has probably been made in the past.

Some combinations of ideas seem strange and unfamiliar. Life assurances with participation in profits—what could be more natural? But annuities with participation in profits?—the association of such discrepant ideas gives rise to all manner of objections in our minds.

Using the stochastic investment model proposed by Wilkie (1995) this paper simulates the progress of a specimen final salary pension scheme over a period of 25 years. Salary experience over the projection period is also assumed to be stochastic. The specimen scheme is assumed to be stable during the projection period with respect to age, pensionable salary in real terms and past pensionable service.

Regular deterministic valuations of the scheme are conducted during the projection period to determine the current level of funding of the scheme on both a discontinuance and an ongoing basis, and also to determine the future contribution rate required to meet the funding objective. The required contribution rate is calculated in accordance with the Inland Revenue surplus regulations and the Minimum Funding Requirement (MFR) introduced in the Pensions Act 1995.

The effect on the level of funding (and, hence, on the size of the required contribution rate) of using different investment strategies and of varying the pace of funding, by adopting both a traditional prudent valuation basis and a more realistic valuation basis, are also explored.

In this paper we consider a discrete time insurance risk model with interest income. Using the recursive calculation method of De Vylder & Goovaerts (1988), recursive equations for the finite time ruin probabilities and the distribution of the time of ruin are derived. Fredholm type integral equations for the ultimate ruin probability, the distribution of the severity of ruin, the joint distribution of surplus before and after ruin, and the probability of absolute ruin are obtained. Numerical results are included.

Mr Elphinstone, in his recent paper to the Faculty of Actuaries, has reawakened interest in the method of graduation devised by Sir Edmund T. Whittaker some 32 years ago. Except for Professor A. C. Aitken who, in a paper( in the Proceedings of the Royal Society of Edinburgh and a note in the Transactions of the Faculty of Actuaries, gave a brilliant alternative solution of the equations on which Whittaker's method depends, English and Scottish writers have paid little attention to the method. Robert Henderson's paper published in 1924 stimulated American actuaries, and their investigations have continued up to the present time. The book by Kingsland Camp (reviewed J.I.A. lxxvii, 327) gives numerous practical developments of Robert Henderson's work. Students should not overlook a most valuable paper by Charles A. Spoerl which deals comprehensively with almost every aspect of the subject.

This paper investigates incentives and disincentives for risk reporting practices by global insurance companies. We examine various arguments for and against risk reporting, whether voluntary or compliance in nature. An important issue is whether reporting is dominated by shareholder, regulatory or managerial incentives. We evaluate whether current reporting practices are consistent with either political visibility, cultural effects or idiosyncratic managerial incentives. Our empirical analysis is based on (1) a content analysis of disclosures contained in annual reports of a sample of European, Asian and US global top 25 insurers between 2006 and 2012 and (2) a survey of internal business reporting practices. We re-characterise a disclosure index from prior research to examine the relation between the extent of risk disclosure and various managerial, agency and other characteristics. We predict that the extent and nature of risk disclosures depends on cultural imperatives and managerial incentives.

1.1 Lloyd's and the rest of the London market underwrite a significant part of the world's insurance and are a dominating influence on insurance world-wide. This paper looks at the data which is collected primarily for reserving purposes inside the market—or rather, the paper looks at some new and unusual but very simple ways of looking at that data. Experience is showing that these simple methods are proving to be more powerful aids to underwriters and auditors than was envisaged when they were first invented. They are graphical and hence easy to ‘see’.

Richard Witt's Arithmeticall Questions, published in 1613, was a landmark in the history of compound interest. In a previous paper (J.I.A. 96, 121) I have described the book and attempted to show why it is so important.

This article sets out some information about Witt's life, which has come to light as a result of research done since the previous article (when very little was known about him). Then follows a discussion of some of the books on compound interest which were published later in the seventeenth century. These not only help to fill in the practical background but also show how the techniques came to be more widely known and how problems arose when interest rates were reduced. It is worth noting that there was an average inflation rate of around 1% p.a. during the first half of the century and an average inflation rate of nil, or even a slight deflation, during the second half (Birks & Morrell, 1976; Mitchell & Deane, 1962). Thus, to a very considerable extent, the interest rates used in calculations were real rates of interest.

1.1 The basic task of actuarial valuation is to compare the quantity of assets with the quantity of liabilities. A refinement is to compare qualities as well as quantities.

1.2 The qualities of assets and liabilities are their characteristics of cash flow, duration, growth, price volatility, etc. This note considers a conceptual and mathematical framework for matching in the most general terms.

1.3 Insurance work in the United Kingdom uses the notion of reserves for mismatching. Pension fund valuations in the U.K. also tend to use a notion of matching when considering the actuarial value placed on the fund.

It is commonly known that in calculating an annuity on three joint lives, two of the lives are made to count as one life of the same annuity value; and that the result is approximately true. Twenty years ago (Phil. Mag., Nov., 1839), I showed that if the law of mortality explained by Mr. Gompertz were accurately true for the whole of life, this substitution of one life instead of two would also be accurately true. I now repeat the same proposition in a more general form.

1.1. In a recent paper, Pollard(1) introduced the morbidity-mortality table as a model for measuring the interaction between morbidity and mortality of chronic degenerative conditions like breast cancer and lung cancer. This device consists essentially of two double decrement tables: for example, persons either remain free of breast cancer for life or depart from the breast cancer-free group by incurring breast cancer or by dying from other causes; those who incur breast cancer either remain alive with it until they die from it or die from other causes. Clearly this model is very similar to the combined marriage-mortality table which is referred to briefly in U.K. actuarial texts(2). Neither of these models, however, allows for increments, for example recoveries from breast cancer in Pollard's morbidity-mortality table. In recent years one of the major advances in the theoretical development and practical construction of life tables has been the incorporation of increments. A guide to this methodology is provided here with particular emphasis on the measurement of incidence and prevalence of disease. Further applications are given in an accompanying paper, to appear in Volume 111(3).

This paper examines the political economy of regulation, reviewing market socialist, neo-classical and public interest approaches to regulation and analysing the development of financial services and insurance regulation in these frameworks. However, the paper suggests that these approaches do not capture properly many of the features of a market and the behaviour of regulators. Public choice theory is discussed, and it is concluded that there has not been significant capture of the regulatory process by interest groups. Austrian economics is proposed as a possible framework within which to analyse markets and regulators. It is concluded that there is prima facie evidence to suggest that the Austrian view of the market is realistic and that regulation in insurance markets can have unforeseen and undesirable effects. The author also concludes that, until 1970, insurance regulation did not deviate from principles which are appropriate if either a public choice or Austrian view is taken. However, the Financial Services Act 1998 and the Pensions Act 1995 do deviate from those principles.

This paper was written at the request of the Life Research Committee of the United Kingdom Actuarial Profession's Life Board. It concerns the valuation of U.K. with-profits business, with particular attention to the market-consistent ‘realistic reporting’ basis currently being used in the U.K. by the regulator, the Financial Services Authority (FSA). The paper surveys recent regulatory activity concerning the development and introduction of the new valuation approach, and puts it into the context of a survey of alternative methodologies, both deterministic and stochastic. The particular issues arising when considering prudential solvency are discussed, and various approaches are reviewed and compared with market consistent methods. Numerical examples are given, which demonstrate potential issues (regarding comparability and consistency) with the FSA's proposed approach — in particular the sensitivity of results to model calibration. The authors support the FSA's move to a stochastically-based framework for solvency measurement, but highlight some issues which need to be taken into account.

The paper firstly examines the way in which U.K. mutuals operate and the forces which are leading mutuals to consider demutualisation. Demutualisation is normally accomplished by a Scheme of Transfer under Section 49 of the Insurance Companies Act 1982. The role of the directors and actuaries is discussed, including the impact of the Institute's latest Guidance Note (GN15).

The protection of policyholders' reasonable expectations, the value of membership rights and the basis of dealing with any orphan surplus are the central problems. The paper examines them in the context of both the open fund and closed fund situation and shows how they may be resolved.

A simple model is used to project the financial position of both an open and closed fund in a demutualised company. The relative advantages and disadvantages of each indicate that different courses of action may be appropriate for mutuals in differing financial positions.

This subject, as it left the hands of Simpson, Halley, Dodson, &c., is fully discussed in the appendices of Francis Baily's work on interest and annuities. These, with Milne's note on the subject (vol. ii., p. 680), Jones's notice of the problem, and the various modes of approximation announced in the pages of this Journal, give all I have found written about the matter in modern times. Referring to the citations in Baily for the history of the question subsequent to 1680, I give what I have found in previous time; and I add a few new formulæ for consideration. The problem is, I doubt not, of infrequent occurrence. It never occurred to myself to want more than a look at the tables would furnish; but it may be suspected that, as the requirements of business become closer, inverse problems will acquire more importance than they now possess.

In a world of transition for all our disciplines, actuaries can get and keep ahead of the changes by, first, getting our thinking right. Right behaviour and actions will follow. We will think about the needs of our employers and clients and present our findings more in the business context; we will look through their needs to the needs and interests of their employees and customers. We will grasp financial economics and learn banking thinking. The profession will raise issues of public interest and inform the debate.