Astin is formally twenty years old, or should I say young, and the occasion of the 13th Colloquium being held in the country where it was constituted seems a very suitable opportunity for making a record of the ten years prior to its formal constitution. This is a personal account and sets out facts and impressions which are now becoming coloured by the vagaries of memory; others will have their own impressions of some of the events and I hope will be stimulated to correct any biasses or to supplement the historical record.

Inevitably this record will not be complete and I apologise in advance for any significant omissions. Over the years I have accumulated a large mass of correspondence and had hoped to codify this in anticipation of this article but unfortunately a series of complications arising from my move to a part of rural England as a further stage in my retirement programme have delayed sorting through the mass of paper.

My interest in non-life insurance was first stimulated when I was involved in the early 1930's in an analysis of the results of Fire and Auto Property business written in the US. This brought me face to face with the differences between the UK and US approach to profit measurement, in particular the real meaning of unearned premiums. The conventional UK method of basing the provision for unexpired risks on 40% of the premiums written during the year led to significant distortion in the emergence of profits (or losses) with an increasing volume of business, a large proportion of which was for periods of three years. Equally the US method of basing a statutory result without any allowance for the equity in the unearned premiums led to further distortions of the true profit, quite apart from the practice, then permitted, of substantial portfolio reinsurance transactions at the close of accounting periods.

The original paper with this title was published in 1968, following presentation at a Casualty Actuarial Society meeting. This is another up-date of indexes in the economic model—first report of 1976 and a forecast for 1977. These LPI indexes measure economic factors affecting loss and loss adjustment settlement costs which are incurred after claims have been reported. The indexes measure direct claims costs and not the reinsured excess losses which would be more adversely affected by inflation.

This is a Claims Market Place concept of the loss settlement function of the insurance company. Claims Costs (our economic cost of production) result from purchasing of services under unusual circumstances in controversial, severe, hasty and often emergency situations. Claims settlements can take place in court rooms, lawyers' offices, repair garages and hospitals. The legalistic atmosphere is often one of friction and excessive demand rather than of a normal commercial esprit de corps. The procurement of these claims services requires dealing with high cost furnishers of services: doctors, clinics, hospitals, lawyers, repair garages or body shops, building trades, house furnishings.

Several “short cut” methods exist to approximate the total amount of claims ( = χ) of an insurance collective. The classical one is the normal approximation

where and σx are the mean value and standard deviation of x. Φ is the normal distribution function.

It is well-known that the normal approximation gives acceptable accuracy only when the volume of risk business is fairly large and the distribution of the amounts of the individual claims is not “too dangerous”, i.e. not too heterogeneous (cf. fig. 2).

One way to improve the normal approximation is the so called NP-method, which provides for the standardized variable a correction Δz

where

is the skewness of the distribution F(χ). Another variant (NP3) of the NP-method also makes use of the moment μ4, but, in the following, we limit our discussion mainly to the variant (2) (= NP2).

If Δz is small, a simpler formula

is available (cf. fig. 2).

Another approximation was introduced by Bohman and Esscher (1963). It is based on the incomplete gamma function

where

Experiments have been made with both formulae (2) and (4); they have been applied to various F functions, from which the exact (or at least controlled) values are otherwise known. It has been proved that the accuracy is satisfactory provided that the distribution F is not very “dangerous”.

In this paper, the establishment of a new insurance organization, the International Insurance Fund (IIF), is proposed. This organization should undertake to deal with extra-hazard risks which are beyond the capacity of both the commercial insurance industry and national governments. It is proposed that the IIF be designed along the basic lines of the International Monetary Fund (IMF) and its sister organizations.

The hypothetical scope of the IIF operations during recent years is illustrated. Certain practical aspects of its actual operations are discussed; some of them call for further examination.

Presented by the Central American Actuarial Association (Asociacion Acturial Centroamericana) to the 13th ASTIN Colloquium.

The Asociaciôn Actuarial Centroamericana (AAC) is a grouping of Actuaries from the Central American Republics of El Salvador, Guatemala, Honduras, Nicaragua, Costa Rica and Panama. The AAC is a contributing ASTIN member of the International Actuarial Association.

Earthquakes have been a constant scourge of mankind. Central America has not escaped this phenomenon, indeed the territory has been most affected by them precisely because of its condition as an isthmus that serves as a fragile union between the continental land masses of North and South America, and in consequence being subject to disturbances by the displacement of the continental plates. Our lands abound with beautiful volcanoes, which have also contributed to local seismic activity. Whatever their origin, the earthquakes that have struck our country have left their share of destruction of lives and property.

In Annex 1 a table is presented, showing a history of seismic activity and volcanic eruptions in the countries on the Caribbean Platform, in which we can appreciate in detail the catastrophes that occurred from the XVI Century until 1976.

Earthquakes and Windstorm can range in size from small easily insurable instances up to full scale Natural Disasters. This note is particularly concerned with the problem of forecasting, rating and insuring earthquakes and windstorm at the natural disaster end of this scale.

Before we tackle the peculiar problems of natural disaster insurance it is worth having a look at why insurance works so well in practice.

Is it because actuaries and statisticians have precisely measured the statistical risks involved, and have developed a detailed and complex mathematical approach to insurance, a true “Technical Basis” for Insurance? Or is it really quite simple?

A quotation (the first of many) from R. Heller [1] is relevant.

“The great and fabled business empires with hardly an exception were built… on irresistable ideas of elemental simplicity.”

Insurance is one of these great empires, and some of the simple ideas which may explain why insurance works so well are suggested below.

Japan is not only a well-known earthquake prone country, but also a land very liable to damage by windstorm, flood, tidal wave and highwater. Especially, it is visited every year by typhoons or tropical cyclones. These occur during the period from early summer to autumn with accompanying heavy rains, and severe damage is often suffered. Most of the serious disasters result from the following causes.

a) Flood from a rapid small river in mountainous areas or landslide occurring there.

b) Innundation of a large plain area caused by the collapse of embankments following heavy rain.

c) Highwater or tidal wave in a harbour or a bay, which is often caused by the visit of a typhoon particularly at full tide.

Generally speaking, damage by the wind is much less in severity than that by flood, tidal wave or highwater.

These natural calamities occur every year, but the extent of the damage differs greatly from year to year. Taking an example of the damage to buildings and contents during 10 years from 1965 to 1974, the largest annual damage estimated for the whole country was ¥ 161.875 million (approx. U.S. $ 578 million), the smallest ¥ 9.398 million (approx. U.S. $ 33,6 million) and the average ¥ 58.561 million (approx. U.S. $ 209 million). (These are the original figures not adjusted for inflation. Also, they do not include the damage to outdoor objects such as roads, bridges, railways, communication facilities, electricity facilities and farms). The greatest windstorm damage in recent years was brought about by the “Bay of Ise Typhoon” in September 1959, at which 153.893 buildings were lost or seriously damaged, 5.101 persons were killed or went missing and 2.430 ships were lost.

Japan is one of the most earthquake-prone countries in the world and a considerable volume of earthquake insurance is written by private insurers. Therefore, a report on earthquake insurance in Japan has been prepared for the 13th ASTIN Colloquium.

We will first summarise, from recent results of seismological studies, the matters which would form the basis for a study of earthquake insurance, and then explain how this insurance actually works in Japan.