INSURANCE AND ACTUARIAL SCIENCE

Actuarial science is in effect one of the first applications of probability theory and statistics to risk analysis. Tetens and Barrois, already in 1786 and 1834respectively, were attempting to characterize the ‘risk’ of life annuities and fire insurance and on that basis establish a foundation for present-day insurance. Earlier, the Gambling Act of 1774 in England (King George III) laid the foundation for life insurance. It is, however, to Lundberg in 1909, and to a group of Scandinavian actuaries (Borch, 1968; Cramer, 1955) that we owe much of the current mathematical theory of insurance. In particular, Lundberg provided the foundation for collective risk theory. Terms such as ‘premium payments’ required from the insured, ‘wealth’ or the ‘firm liquidity’ and ‘claims’ were then defined. In its simplest form, actuarial science establishes exchange terms between the insured, who pays the premium that allows him to claim a certain amount from the firm (in case of an accident), and the insurer, the provider of insurance who receives the premiums and invests and manages the moneys of many insured. The insurance terms are reflected in the ‘insurance contract’ which provides legally the ‘conditional right to claim’. Much of the insurance literature has concentrated on the definition of the rules to be used in order to establish the terms of such a contract in a just and efficient manner. In this sense, ‘premium principles’ and a wide range of operational rules worked out by the actuarial and insurance profession have been devised. Currently, insurance is gradually being transformed to be much more in tune with market valuation of insurable contracts and financial instruments are being devised for this purpose. The problems of insurance are,of course, extremely complex, with philosophical and social undertones, seeking to reconcile individual with collective risk and individual and collective choices and interests through the use of the market mechanism and concepts of fairness and equity. In its proper time setting (recognizing that insurance contracts express the insured attitudes towards time and uncertainty, in which insurance is used to substitute certain for uncertain payments at different times), this problem is of course,conceptually and quantitatively much more complicated. For this reason, the quantitativ approach to insurance, as is the case with most financial problems, is necessarily a simplification of the fundamental issues that insurance deals with. Risk is managed in several ways including: ‘pricing insurance, controls, risk sharing and bonus-malus’ Bonus-malus provides an incentive not to claim when a risk materializes or at least seeks to influence insured behaviour to take greater care and thereby prevent risks from materializing. In some cases, it is used to discourage nuisance claims. There are numerous approaches to applying each of these tools in insurance. Of course, in practice, these tools are applied jointly, providing a capacity to customize insurance contracts and at the same time assuming a profit for the insurance firm. In insurance and finance (among others) we will have to deal as well with special problems, often encountered in practical situations but difficult to analyse using statistical and analytical techniques. These essentially include dependencies, rare events and man-made risks. In insurance, correlated risks are costlier to assume while insuring rare and extremely costly events is difficult to assess.

Earthquake and tornado insurance are such cases. Although, they occur, they do so with small probabilities. Their occurrence is extremely costly for the insurer,however. For this reason, insurers seek the participation of governments for such insurance, study the environment and the patterns in weather changes and turn to extensive risk sharing schemes (such as reinsurance with other insurance firms and on a global scale). Dependencies can also be induced internally (endogenously generated risks). For example, when trading agents follow each other’s action they may lead to the rise and fall of an action on the stock market. In this sense, ‘behavioural correlations’ can induce cyclical economic trends and therefore greater market variability and market risk. Man-made induced risks, such as terrorists’ acts of small and unthinkable dimensions, also provide a formidable challenge to insurance companies. John Kay (in an article in the Financial Times, 2001) for example states: