After I had written the first draft of an article on the above subject, my attention was drawn to two articles by Mr. King “On Mortality amongst Assured Lives.” I had felt much diffidence in saying anything having the appearance of adverse criticism of the valuable works issued by the Institute; but now that I observe that Mr. King's articles, which are in some measure founded on opinions similar to my own, have been received with marked approval, I feel more confidence in stating plainly what appear to me defects in the HM and HM(5) Tables. But whatever I may say respecting them, I trust that my assurance will be accepted that I entertain feelings of the highest respect for the eminent knowledge and ability of the distinguished persons concerned in their preparation, with the most hearty and grateful appreciation of the benefits which they have conferred on the profession. I need hardly say that nearly all that I know of the subject of mortality amongst assured lives, is due to them.

This discussion meeting was on the subject of business ethics, with particular reference to the work of actuaries.

As an introduction to the meeting, copies of the paper, ‘Business Ethics: the New Bottom Line’, by Sheena Carmichael, were distributed to members of the Institute.

Sheena Carmichael is the director of ETHOS, a consultancy dedicated to helping organisations identify and manage ethical issues. She is a research associate at the European Institute of Business Ethics at Nigenrode University in the Netherlands.

The paper ‘Business Ethics: the New Bottom Line’, was published in 1995 by Demos, which “is an independent think-tank committed to radical thinking on the long-term problems facing the United Kingdom and other advanced industrial societies.

It aims to develop the ideas — both theoretical and practical — that will shape the politics of the 21st century, and to improve the breadth and quality of political debate.” It is a registered charity.

The paper has not been reproduced in British Actuarial Journal, but further information can be obtained from:

Demos, 9 Bridewell Place, London, EC4V 6AP; telephone: 0171 353 4479; facsimile, 0171 353 4481; email, [email protected]

In this paper we present many investigations into the results of simulating the process of hedging a vanilla option at discrete times. We consider mainly a ‘maxi’ option (paying Max(A, B)), though calls, puts and ‘minis’ are also considered. We show the sensitivity of the variability of the hedging error to the actual investment strategy adopted, and to the many ways in which the simulated real world can diverge from the assumed option pricing model. We show how prudential reserves can be calculated, using conditional tail expectations, and how net premiums or fair values (which we present as the same) can be calculated, allowing for the necessary prudential reserves. We use two bond models, the very simple Black-Scholes one and a less unrealistic one. We also use the Wilkie model as an even more realistic real-world model, allowing for many complications in it to make it more realistic. We make observations on the important difference between real-world models and option pricing models, and emphasise the latter as the way of getting hedging quantities, and not just option prices.

This paper seeks to establish good practice in setting inputs for operational risk models for banks, insurers and other financial service firms. It reviews Basel, Solvency II and other regulatory requirements as well as publicly available literature on operational risk modelling. It recommends a combination of historic loss data and scenario analysis for modelling of individual risks, setting out issues with these data, and outlining good practice for loss data collection and scenario analysis. It recommends the use of expert judgement for setting correlations, and addresses information requirements for risk mitigation allowances and capital allocation, before briefly covering Bayesian network methods for modelling operational risks.

This discussion paper was produced by a Working Party in April 1997 to put forward some possible ways of improving the United Kingdom financial regulatory process. It was written to contribute to the expected post General Election debate on this topic. Although the new Government announced plans in May 1997 for a new Securities and Investment Board (SIB) with statutory powers, this has not reduced the value of this discussion paper which raises some wider issues on methods of regulation.

The paper excludes the supervision and regulation of banks, building societies, insurance companies and exchanges and concentrates on areas that directly affect the public on an ongoing basis. It looks at the expectations of the main parties involved in regulation, the theory and practice of regulation, opportunities and concerns, and concludes with a summary of key issues for discussion. The thrust of the paper is that self regulation should be replaced by statutory regulation and that the present ‘prescriptive’ regulatory process should be replaced by one based on ‘outcomes’ supported by guidance.

The market for green bonds, and environmentally aligned investment solutions, is increasing. As of 2022, the market of green bonds exceeded USD 2 trillion in issuance, with India, for example, having issued its first-ever sovereign green bonds totally R80bn (c.USD1bn) in January 2023. This paper lays the foundation for future papers and summarises the initial stages of our analysis, where we try to replicate the S&P Green Bond Index (i.e. this is a time series problem) over a period using non-traditional techniques. The models we use include neural networks such as CNNs, LSTMs and GRUs. We extend our analysis and use an open-source decision tree model called XGBoost. For the purposes of this paper, we use 1 day’s prior index information to predict today’s value and repeat this over a period of time. We ignore for example stationarity considerations and extending the input window/output horizon in our analysis, as these will be discussed in future papers. The paper explains the methodology used in our analysis, gives details of general underlying background information to the architecture models (CNNs, LSTMs, GRUs and XGBoost), as well as background to regularisation techniques specifically L2 regularisation, loss curves and hyperparameter optimisation, in particular, the open-source library Optuna.

The advances which have been made in valuation methods were brought home very forcibly to my mind when perusing the records of a valuation made many years ago.

During the past 50 or 60 years the valuation of complicated benefits has been, generally speaking, rendered a comparatively easy task, thanks to the energies of members of this and of other Actuarial Institutes—the Law of Makeham, to take one instance, has been the means of simplifying the solutions of a great number of difficult problems—and the numerous approximations to various intricate expressions, which have appeared from time to time in the pages of the Journal, have further lightened the labour of valuations.

In this paper we present an approach to the graduation of select mortality data and we illustrate this approach by graduating the CMIB's data for Female Permanent Assurances 1979–1982. The difference between our approach and that of the CMIB is that we graduate simultaneously by attained age and duration since selection.

Lidstone's formula for approximating to the premium for a joint-life endowment assurance is

It has been found empirically that the greater the disparity in age the less accurate is the approximation. There is no such progressive loss of accuracy as the period of assurance lengthens.

The existing theory and practice of Annuities and Assurances, and the tables ordinarily constructed for the purpose of expediting the various computations relating to the same, are radically founded on annual payments, or upon a series of mathematical values which appertain to certain annual periods that are specifically defined. Indeed, the methods employed are not strictly applicable unless the prescribed condition of annual periodicity is realized or assumed; and this, in fact, is the reason why assurances, as well as annuities, are necessarily supposed to be payable on the exact completion of one of the recurring periods, viz., at the end of the year of age in which the death takes place.

Some time ago, the writer had occasion to examine the principal methods adopted by life assurance companies in the distribution of surplus, and particularly the plan which is known as “Sprague's Method”, from the name of its inventor, Dr. Sprague, or the “Equity and Law Method”, from the name of the company to which it was first applied. The plan is at present employed by comparatively few British offices, but it has recently been adopted by several companies in substitution for systems previously in vogue, and it appears to be rapidly growing in theoretical importance as a standard by which to test the effect of other systems of distribution. Nevertheless, it would appear that, apart from the brief description of the method originally given by Dr. Sprague (and quoted below), there is no systematic discussion of the principles of the method in the pages of the Journal of the Institute of Actuaries, and it is therefore thought that a few notes respecting some of the points which arise in connection with the practical application of the method may be of service to those who are studying the subject, but who may share the experience that little information is to be gleaned from the Journal.