CHAPTER XI THE MEASUREMENT OF RISK IN LIFE INSURANCE By BRUCE D. MUDGETT THE THEORY OF PROBABILITY Insurance has been defined as the institution which eliminates risk or which substitutes certainty for uncertainty. The occurrence of events insured against cannot wholly be prevented, but the uncertainty of financial loss through such occurrences can be eliminated by distributing the loss over a group. Thus a man cannot be sure whether or not his house will burn even if he use all the preventive measures known. If the house burns the property is lost and forever gone that much material value has been actually destroyed. But it is not necessary that the owner should stand the entire loss. Before the fire occurred it was not known whether his house would burn or some one's else and he could agree with other owners of houses that they would all contribute to a common fund from which any unfortunate owner who lost his house by fire should be recompensed. Thus instead of the loss falling on one it can be divided equally among all. This is the essence of insurance and it illustrates the meaning of the statement that insurance is the elimination of uncertainty or the replacement of uncertainty by certainty. The common contribution to the fund above referred to constitutes the certain loss and is measured by the premium; the uncertain loss refers to the uncertainty that a particular house will burn. The same situation exists with respect to life insurance. It is not death itself that can be distributed, i.e. parcelled out among a number of insurers, but the financial consequences of death. Man has an earning power during a certain period of his life which is lost to his business or his family by premature death, but it is not known in advance upon whom death will fall prematurely, hence all men can contribute to a fund which will be used to satisfy the business and family needs of those who die early. These two illustrations suggest the possibilities that exist for the application of the insurance principle. In whatever field risk is found to exist, there the principle can be applied. The complete working out of a scientific insurance plan necessitates some method of measuring this risk in order to determine the amount of each individual's contribution to the common fund. The correct measurement of risk, therefore, lies at the foundation of any system of insurance. This accomplishment is rendered possible through the application to statistical data, covering the phenomenon in question, of certain laws developed in the field of mathematics known as the laws of probability, and it will be necessary to state and explain them before proceeding further. The Laws of Probability. The science of probabilities furnishes three principles of which practical use is made in life insurance. They may be called respectively (1) the law of certainty, (2) the law of simple probability, and (3) the law of compound probability. Their use makes possible the description of risk in terms of mathematical values, and the statement of the three laws is as follows: (1) certainty may be expressed by unity, or one; (2) simple probability, or the probability or chance that an event will happen or that it will not happen may be expressed by a fraction; and (3) compound probability, or the chance that two mutually independent events will happen 1 is the product of the separate probabilities that the events, taken separately, will happen. 1 An illustration will serve to make these statements clear. If a box contains twenty marbles and it is known that five of 1 There are laws of compound probabilities, for instance, where the separate events are dependent, but they do not enter into the present discussion. |