A new stream of research proposes how people can increase their income in retirement by pooling their mortality risk. How one of these mortality risk-sharing rules could be implemented in practice, as part of a retirement income scheme, is considered. A potential advantage of the scheme is that a retiree’s housing wealth can be monetised to provide an income stream. This would mean that retirees can continue living in their home, without needing to downsize. It may be most attractive to the millions of single pensioners, particularly those who are “asset-rich and cash-poor”. Other types of assets that could be included and how to mitigate selection risks are assessed. A way of smoothing the raw mortality credits in order to make the scheme more appealing to potential members is proposed. An illustrative premium calculation suggests that the cost of the smoothing is very small compared to the potential attractiveness of an enhanced, smoothed income.

This paper addresses one of the fundamental issues faced by offices in the transacting of with-profits business, namely, the provision of equity-related performance along with maturity guarantees that increase over the lifetime of the policy. The approach commonly followed of using capital to cover the office's investment mismatch risk is considered from an individual policy viewpoint, and, through stochastic modelling, the degree of security represented by different reserve levels identified. An alternative approach using derivatives to provide similar levels of security is then presented and the range of policy proceeds resulting from the two methods compared. While it is recognised that the latter approach may have limited application in practice, the ideas presented could form the basis of a new approach to pricing guarantees under with-profits business that would be consistent with the pricing of current derivative-backed guaranteed products.

The purpose of this paper is to describe a methodology for determining an appropriate structure for time-series models of inflation rates, short-term and long-term interest rates, dividend growth rates, dividend yields, rental growth rates and rental yields and to demonstrate the application of that methodology to the development of a model based on South African data. It is suggested that the methodology used in this paper may be applied to other economic environments.

1.1 In this paper I intend to concentrate on the application of mathematics and the problems faced and (sometimes) solved by such application, rather than on the mathematics itself. That is not to belittle the mathematics in any way, and I would like to acknowledge at the start that the stochastic financial model which underlies the results given in this talk is based on Professor Wilkie's model as detailed in T.F.A.39, 341.

In the article “Mortality”, in the Penny Cyclopæia, the late Professor De Morgan gave the following description of the law of mortality propounded by Gompertz in the paper presented to the Royal Society in 1825. “As this ingenious paper”, says De Morgan, “contains a deduction from a principle of high “probability, and terminates in a conclusion which accords in a “great degree with observed facts, it must always be considered “a very remarkable page in the history of the enquiry before “us…. There is in the human constitution a power of “resisting the effects of disease which increases from birth up to “a certain age, and diminishes from that time forwards.… “Mr. Gompertz assumes that the power to oppose destruction “loses equal proportions in equal times, &c, &c.” Gompertz's theory of mortality, then, is based upon the supposed physiological fact that the living human organism is endowed with a certain recuperative power, becoming (after a few years from birth) ever less and less efficient with the lapse of time, which he terms “the power to oppose destruction”, but which, for brevity, I will call “vital force”, the truth of which supposition is evidently a question for common observation.

This review was undertaken for the Faculty and Institute of Actuaries as part of their programme to encourage research collaborations between health researchers and actuaries in order to understand better the factors influencing mortality and longevity. The authors presented their findings in a number of linked sessions at the Edinburgh conference (Joining Forces on Mortality and Longevity) in October 2009 and contributed to this overview. The purpose is to review evidence for the impact on adult mortality of characteristics of the individual's lifetime socioeconomic or psychosocial environment or phenotype at the behavioural; multi-system (e.g. cognitive and physical function); or body system level (e.g. vascular and metabolic traits) that may be common risk factors for a number of major causes of death. This review shows there is growing evidence from large studies and systematic reviews that these individual characteristics, measured in pre-adult as well as the adult life, are associated with later mortality risk. The relative contribution of lifetime environment, genetic factors and chance, whether these contributions change with age, and the underlying social and biological pathways are still to be clarified. This review identifies areas where further life course research is warranted.

Throughout this century mortality has been declining and if an exponential curve in the Gompertz form μx = bcx is fitted to recent English Life Tables b has been decreasing as we would expect. Between the 1911 Table and the 1951 Table, 105b has fallen from 18 to 6 for males and from 9 to 2 for females. But c has been increasing—from 1·087 to 1·103 for males, and from 1·094 to 1·112 for females. What feature of mortality can it be that has been deteriorating in this scientific age? Has c any counterpart in reality? Or is it just a mathematical by-product of our system of description?

This paper is divided into three parts. Taken together, the three parts intend to provide the reader with an overview of the first 101 years of financial economics, with particular attention on those developments that are of special interest to actuaries. In Section 1, S.F. Whelan attempts to capture the flavour of the subject and, in particular, to give an overview or road map of this discipline, highlighting actuarial input. In Section 2, D.C. Bowie gives a concise and self-contained overview of the Modigliani and Miller insights (or MM Theorems, as they are often known). In Section 3, A.J. Hibbert considers the novel option pricing method proposed by Black, Merton, and Scholes. These two insights are highlights of this newscience, and, in both cases, contradict our intuition.

T.S. Elliot, the mathematically trained poet, described the darkness that intercedes between the idea and the action as the ‘shadow’. There is a shadow to be considered between these insights and their application. The demonstration of the results requires, of course, some idealised circumstances, and therefore the extent and degree of their applicability to the non- idealised problems encountered by actuaries requires some delicate considerations. An attempt is made to outline these further considerations.

In this paper we discuss methods of developing real estate indices, the availability of real estate data, the problems of using published real estate data and how real estate data can be used for stochastic investment modelling for actuarial purposes. In recent years there have been many developments in the collection, presentation and analysis of real estate data that have not found their way into the actuarial literature. We review those developments and suggest and develop ways in which raw real estate investment data can be used for actuarial purposes. We then review the Wilkie real estate stochastic investment model and use the research of real estate finance academics to inform a critique and development of that model. In developing the models, different data sets are used, including data from valuation-based and de-smoothed indices in order to find appropriate parameter estimates. The significance (or otherwise) of the parameter estimates is tested for each of the fitted models and the differences between the fitted models are examined. By reviewing research in the real estate finance field, making use of the latest research and developing original work, the main aim of this paper is to ensure that actuaries have the means to collect, understand and manipulate real estate data for performance measurement and investment modelling purposes.

This paper draws analogies between techniques used to reserve for, control and manage derivatives and techniques used by actuaries in other fields. It concentrates on equity derivatives. It also includes a review of the factors which significantly influence the appropriate size of reserves to hold for a derivatives portfolio. These include the likelihood of market jumps, uncertainty in future market volatility and the size of transaction costs, as well as on more obvious factors like position risk.

This paper reviews the developments in reporting of traditional embedded value and summarises some of the reasons why this is now undergoing change. It considers the purpose of an embedded value calculation and the effect of differing attitudes to risk. It comments on the recently developed European Embedded Value Principles and sets out the main areas where scope remains to apply judgement.

The paper proposes the market-consistent embedded value framework as a way forward to help provide guidance in some of these areas, in particular on the choice of discount rate and on calibration of stochastic techniques used to value embedded options and guarantees. The paper recognises that market-consistent embedded values are in relative infancy and sets out areas for possible future development.

This paper reviews Panjer's recursion formula for evaluation of compound distributions and illustrates how it can be applied to life and general insurance problems.

The paper reviews the underwriting of life assurance and sickness benefits today. It considers both medical and non-medical aspects and how the extra risks should be costed. The paper also deals with financial underwriting. reassurance and the management of death claims. Although the paper presents a ‘state of the art’ picture, it also considers advances via on-line acceptance, expert systems and computer-based training.

In this paper we review three algorithms to calculate the probability of ruin/survival in finite time for the classical risk model. We discuss the computational aspects of these algorithms and consider the question of which algorithm should be preferred.

The paper overviews the application of existing actuarial techniques to operational risk. It considers how, working in conjunction with other experts, actuaries can develop a new framework to monitor/review, establish context, identify, understand and decide what to do in terms of the management and mitigation of operational risk. It suggests categorisations of risk to help analyses and proposes how new risk indicators may be needed, in conjunction with more normal quantification approaches.

Using a case study, it explores the application of stress and scenario testing, statistical curve fitting (including the application of extreme value theory), causal (Bayesian) modelling and the extension of dynamic financial analysis to include operational risk. It suggests there is no one correct approach and that the choice of parameters and modelling assumptions is critical. It lists a number of other techniques for future consideration.

There is a section about how ‘soft issues’ including dominance risk, the impact of belief systems and culture, the focus of performance management systems and the psychology of organisations affect operational risk. An approach to rating the people aspects of risk in parallel with quantification may help give a better overall assessment of risk and improve the understanding for capital implications.

The paper concludes with a brief review of implications for reporting and considers what future work will help develop the actuarial contribution. It is hoped the paper will sow seeds for the development of best practice in dealing with operational risk and increase the interest of actuaries in this emerging new topic.

The Paper is an attempt to suggest a method of estimating the mortality of the future from the records of the past.

In Part I., after a brief discussion of the existing methods of calculating rates of mortality, a new method of employing past results called the “cumulative process” is suggested. The chief distinction between the new method and those already in use lies in the fact that an attempt is made to employ existing knowledge of mortality rates when examining new data. It is claimed for the cumulative process that it is suited to a steadily increasing accumulation of knowledge such as should be the result of systematic mortality studies.

The Objective of Funding

1.1. As every actuarial student is taught:

‘Pay-as-you-go is acceptable for a State pension scheme because the State is, for practical purposes, assured of a continuing existence.’

However:

‘The position is quite different in the case of an occupational scheme, since an employer's business may cease to exist.’

1.2. It seems to us to follow, therefore, that the prime purpose of funding an occupational pension scheme must be to secure the accrued benefits, whatever they might be, in the event of the employer being unable or unwilling to continue to pay at some time in the future. To that end, the contributions would have to be sufficient both to pay the benefits as they fell due for as long as the scheme continued, and also to establish and maintain a fund which would be sufficient to secure the accrued benefits in the event of contributions ceasing and the scheme being discontinued, whenever that might occur.

The Solvency II Directive mandates insurance firms to value their assets and liabilities using market consistent valuation. For many types of insurance business Economic Scenario Generators (ESGs) are the only practical way to determine the market consistent value of liabilities. The directive also allows insurance companies to use an internal model to calculate their solvency capital requirement. In particular, this includes use of ESG models. Regardless of whether an insurer chooses to use an internal model, Economic Scenario Generators will be the only practical way of valuing many life insurance contracts. Draft advice published by the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS) requires that insurance firms who intend to use an internal model to calculate their capital requirements under Solvency II need to comply with a number of tests regardless of whether the model (or data) is produced internally or is externally sourced. In particular the tests include a ‘use test’, mandating the use of the model for important decision making within the insurer. This means that Economic Scenario Generators will need to subject themselves to the governance processes and that senior managers and boards will need to understand what ESG models do and what they don't do. In general, few senior managers are keen practitioners of stochastic calculus, the building blocks of ESG models. The paper therefore seeks to explain Economic Scenario Generator models from a non-technical perspective as far as possible and to give senior management some guidance of the main issues surrounding these models from an ERM/Solvency II perspective.

The approaches to liability valuation, assessment of prudential capital and measurement of profit for life offices are undergoing radical change. A common thread runs through all of these proposed changes — each change represents a move away from traditional actuarial approaches towards a more economically coherent, market-consistent approach. These changes should encourage a general improvement in the life industry's risk management processes. However, they will come at a cost. The measurement of the economic risks generated by the complex guarantees written by life offices is far more difficult than applying the latest resilience test equity fall. This will require a step change in the sophistication of life offices' risk and capital measurement and management know-how. The measurement of value, risk and capital will soon demand the application of ‘stochastic’ modelling tools. In this paper, we explore some of the issues raised by the application of these approaches to the valuation and risk management of with-profits business.