A principal use of logarithms is to solve all the cases of compound interest which are not, without great difficulty, attainable by the rules of common arithmetic. But before we proceed to the practical part, it may, perhaps, not be improper to say something of the foundation or demonstration of the rules we are to give.

In this paper, we explore potential surplus modelling improvements by investigating how well the available models describe an insurance risk process. To this end, we obtain and analyse a real-life data set that is provided by an anonymous insurer. Based on our analysis, we discover that both the purchasing process and the corresponding claim process have seasonal fluctuations. Some special events, such as public holidays, also have impact on these processes. In the existing literature, the seasonality is often stressed in the claim process, while the cash inflow usually assumes simple forms. We further suggest a possible way of modelling the dependence between these two processes. A preliminary analysis of the impact of these patterns on the surplus process is also conducted. As a result, we propose a surplus process model which utilises a non-homogeneous Poisson process for premium counts and a Cox process for claim counts that reflect the specific features of the data.

Presidential Addresses are an opportunity to survey the actuarial landscape, and this one is no exception. The pace of change and scope of work undertaken by actuaries since the President qualified is commented upon. Many of the current and future issues are also aired, from bonus rates and pensions mis-selling to stakeholder pensions and long-term care. Regulation, in a number of areas, is also reviewed. The regular topics of education, examinations and continuous professional development also feature.

This document, consisting of several papers, sets out to provide a basis for discussion among actuaries of the Vision and Values of the United Kingdom actuarial profession. The profession realises that a clear vision and a strong sense of shared values are important attributes of a successful organisation. Following on from the work that has been done already in recent years on the mission and strategic aims of the Faculty and the Institute, several issues have been highlighted and need to be resolved so that the profession can move forward into the future.

In this document the Councils have stated what they consider to be the key elements of their vision for the profession in 2020 and of the values that they think the profession should have. These and the issues that arise from them are expanded in this document to give a focus for discussion.

Unit trusts originated in the United Kingdom in the second half of the nineteenth century, but an early court ruling that unit trusts were not legal resulted in all but one unit trust changing to the form of investment trusts. Although the court ruling was later reversed, little further headway was made by the unit trust movement until after the Great Crash of 1929.

Not much seems to have been written on the subject of the Mortality of the West Indies as compared with that of the mother country. The following contribution, being the experience of the Scottish Amicable Life Assurance Society in these colonies during the last thirty years, may therefore, perhaps, be useful as well as interesting. The Directors of the Society have cordially adopted the suggestion that the figures should now be made public.

This paper had its origin a year or two ago in an investigation entered upon with an object which has since fallen into abeyance. At that time, it being desired to obtain a thoroughly well-graduated table of mortality giving a favourable view of human life, attention was directed to the Carlisle Table, and sundry attempts were made to remove its irregularities.

Many of the experiments then tried would not now be of any public interest, but the effort to use Mr. Makeham's formula brought out a few facts which it is perhaps worth while to record; and, at any rate, whatever may be thought of the present notes, the authors do not consider themselves to be guilty of any impropriety in bringing forward for discussion once more the practical employment of Mr. Makeham's expression for the law of human mortality.

They are the more emboldened to suggest this subject for debate, in that Mr. Walford, at a late meeting, announced that the formula was found in America to give perfectly satisfactory results when applied to a table formed from the experience of assured lives on that continent.

The first step in the original investigation was to graduate the Carlisle Table (as published by Mr. Milne) by means of Mr. Woolhouse's formula; and as the resulting curve was not entirely free from roughness, the process was repeated. The changes introduced by the second graduation were insignificant, but the table produced was one of very great smoothness, although there was a wave-like form observable in the succession of the values of some of the functions.

There are many references in the pages of the Journal to Old Age Pensions, and in view of the Act of last year the subject—from a financial and statistical aspect—may be discussed without transgressing on questions of State policy. I therefore venture to submit the following notes of some of the financial and statistical questions involved, stimulated in so doing by Mr. G. F. Hardy's statement in his Presidential Address, that he believed our most important work lies in the proper application of actuarial principles to the many practical questions which arise from time to time.

Old age pensions ranging from 1s. to 5s. a week according to the yearly means of the pensioners are granted to British subjects resident in the United Kingdom who have attained the age of seventy years, provided their yearly means do not exceed ￡31 10s., and provided they are not disqualified on the ground of Poor Law Relief, imprisonment, or the other reasons set forth in Section 3 of the Act.

The UK has seen a significant transition from Defined Benefit (“DB”) to Defined Contribution (“DC”) for occupational pension saving. The planned automatic enrolment program starting in 2012 is expected to increase the use of DC. The main features of DC are that investment risk falls onto the individual during the pre-retirement phase and that there are no guarantees as to investment returns or the level of pension. In July 2012, Steve Webb, the Pensions Minister, challenged industry to think hard about meeting the need for more certainty about pension savings in DC plans and to consider providing an affordable ‘Money Safe’ guarantee where the member would get back at least the nominal value of their contributions (individual, employer and tax relief). This paper explores whether this is viable for the mass market.

This paper considers five issues arising from guaranteed annuity options in pension policies issued by United Kingdom life assurance companies. These are the investment strategies for such options, the implications for bonuses on with-profits policies, the measurement of the solvency position and preparation of accounts of the companies concerned, and the policy debate on compulsory annuitisation. In particular, the paper highlights the impact of improving mortality on the value of options, comments on the House of Lords judgment in the Equitable Life case, and suggests additional disclosures in the accounts of life assurance companies.

The Nested Binomial Model presented in this paper is a new approach to modelling mortality and survival in humans and other species that seeks to reconcile individual life course risk trajectories and those population mortality patterns that arise from inter-individual heterogeneity. In describing individual trajectories it partitions mortality risk into two main elements: ‘redundancy’ and ‘interactive risk'. Interactive risk is volatile, increasing or decreasing with time and circumstance, while redundancy is a quantity which declines in a linear and largely invariable fashion throughout life. Although a biological correlate for redundancy is not identified, this assumption allows strikingly realistic modelling of mortality and survival curves, late-life mortality deceleration, Strehler-Mildvan correlation, mortality plateaux and slowing of mortality. Simple assumptions with regard to heterogeneity of parameters within the model allow close approximation to the entire human mortality curve, and provide a rationale for observed and otherwise paradoxical population mortality phenomena. As such, it fulfils biodemographic criteria for a comprehensive theory of ageing. Future challenges are to reconcile its theoretical structure with empirical findings in the biology of ageing and to render it in a form that can become a usable actuarial tool.

This paper introduces and demonstrates the use of quantum computers for asset–liability management (ALM). A summary of historical and current practices in ALM used by actuaries is given showing how the challenges have previously been met. We give an insight into what ALM may be like in the immediate future demonstrating how quantum computers can be used for ALM. A quantum algorithm for optimising ALM calculations is presented and tested using a quantum computer. We conclude that the discovery of the strange world of quantum mechanics has the potential to create investment management efficiencies. This in turn may lead to lower capital requirements for shareholders and lower premiums and higher insured retirement incomes for policyholders.

In this paper we investigate the effectiveness of the Minimum Funding Requirement (MFR) (pre-1999 version) under random future investment conditions. In particular, do the various liabilities calculated under the MFR deliver a suitable level of security to pension scheme members?

The paper considers active (and deferred) members and current pensioners separately.

For active members, Monte Carlo simulation is used to compare how the proceeds arising from investment of the pre-1999 MFR liability in an equity-backed personal pension would compare with the deferred pension promised by the scheme. It is found that, while there may be the intended 50% chance that the personal pension has a better outcome, there are very substantial downside risks for younger members. Investment strategies based upon index-linked gilts are shown to result, on average, in lower personal pensions, but they provide an extremely effective means of limiting the downside risks.

For pensioners, Monte Carlo simulation is used to find the distribution of the initial amount of assets required to pay off precisely the pension liabilities as they arise. This investigation considers the effectiveness of the 12-year rule and different investment strategies. The 12-year rule in combination with an equivalent investment strategy is shown to provide reasonable security for a typical group of pensioners. However, if investments are restricted to an appropriate mixture of gilts then the level of security for pensioners is much increased. In particular, we investigate the use of value-at-risk reserves. It is found that 95% value-at-risk reserves are lower for a mixed conventional/index-linked gilts strategy than a mixed gilts/equity strategy.

It is argued, because of the high degree of downside risk, that there is no place in MFR calculations for high, anticipated equity returns. Instead rates of interest should be based solely upon fixed-interest and index-linked gilt yields.

Traditional and standard discounted cash flow valuation techniques are unable to deal with a variety of options contained in lease contracts. In the United Kingdom the most important embedded option is the upward-only rent review. This becomes more valuable to the landlord in an era of low demand and low inflation, as nominal market rents are more likely to fall. Lease contracts are freely negotiated between landlord and tenant, and alternative forms of rent review clause would fundamentally change the investment characteristics of property. Many other less common options also exist in lease contracts and these create further valuation difficulties. It is essential that property valuation techniques be developed that explicitly value the options in lease contracts.