Schedule 1 of the Insurance Companies Act 1982 defines Permanent Health Insurance (PHI) as a class of Long Term insurance business being “… contracts of insurance providing specified benefits against risks of persons becoming incapacitated in consequence of sustaining injury as a result of an accident or of an accident of a specified class or of sickness or infirmity being contracts that:

(a) are expressed to be in effect for a period of not less than five years, or until the normal retirement age for the persons concerned or without limit of time, and

(b) either are not expressed to be terminable by the insurer, or are expressed be so terminable only in special circumstances mentioned in the contract.”

The fundamental features of PHI as developed in the U.K. are therefore:

(a) It provides specified benefits in the event of ill health.

(b) Cover may not be cancelled by the insurer (except under special circumstances described in the policy document) and hence the insurance is ‘permanent’.

The subject of valuation is one of the most important, and at the same time most difficult, of all the problems faced by actuaries.

The traditional approach to the subject has centred on discussion of the relative merits of the net premium and bonus reserve methods of valuation, and on the inherent conflict between valuation as a means of demonstrating solvency and valuation as a tool for ensuring a smooth emergence of surplus in accordance with the need to declare uniform reversionary bonuses. This approach is covered in the well-known papers by Redington (2) and Skerman (3) (4) and forms a significant part of the course of reading for examination subject 8 (formerly B2).

Bonus reserve methods are, typically, ‘active’ methods of valuation in which all relevant parameters, including expenses and future bonuses, are given values close to their expected values. The premium valued is the office premium, and assets are usually valued at market value or by discounting expected investment income. Because actual conditions are always changing, an active valuation method tends to lead to frequent changes of basis and this introduces an element of volatility to the results which can, in consequence, be difficult to interpret. Nevertheless, because of the emphasis on using realistic values for all parameters, it is commonly believed that bonus reserve methods are particularly appropriate for investigations into solvency, especially when external conditions are changing rapidly, and in determining appraisal values.

As far as we are aware there have been no life insurance demutualizations in the U.K. in recent times, that is conversions from mutual to proprietary form. There has been movement in the other direction: in the 1960's a number of U.K. proprietary companies converted to mutual form to escape the unwelcome attentions of the corporate raiders of the time.

In the U.S. and South Africa however, the two countries which give us the demutualization examples in this paper, there have been in recent years a number of significant demutualizations. In the next chapter we give a sketch of the background to demutualization in these countries.

In Section 3 we explore why a mutual might wish to undergo such a lengthy, costly and probably painful process. The motivation will vary from country to country, depending on the particular economic and institutional background. We have tried to be as general as possible.

The burden of legislation upon authorized insurers in the U.K. continues to grow and this is particularly true for the statutory valuation. In recent years regulations have been introduced to cover such matters as the valuation rates of interest, the provision for changes in investment conditions and the setting up of solvency margins.

The purpose of this paper is to summarize some of the more important aspects of the Regulations and comment upon their interpretation with reference to current practice. A substantial part of the paper is concerned with the provision for changes in investment conditions. Some implications for financial control and product pricing are also mentioned.

The paper will concentrate on the valuation of liabilities and is written in the context of assets taken in accordance with the asset valuation regulations, that is to say broadly at market value. Most of the paper is addressed to conventional business but a few comments on linked business are included. The material is discussed under various headings but is so interdependent that it is difficult to concentrate on one aspect without impinging on several others.

Hogg and Klugman use the truncated Pareto distribution with probability density function

where δ≥0 is specified and α > 0 and λ > 0 are unknown parameters, to describe insurance claims. This is fitted first of all by the method of moments, using the estimators

and

where is the mean of a simple random sample, and the (biased) variance

The authors then suggest, on pp. 113–16, that these estimates be used as starting values in a Newton iteration to get the maximum likelihood estimates of the parameters, but this technique can fail as a result of convergence problems. The object of this note is to show that this has led Hogg and Klugman to underestimate seriously the area in the tail of a fitted loss distribution, and to discuss a method of circumventing this difficulty.