INSURANCE. 680 INSURANCE. the loss bears to the value of the whole interest of the insurance on the property. The amount stated on the face of the policy is the niaxlniuni amount for which an insurance company may become liable. In some forms of insurance, as in life, accident, and sickness in- surance, the amount stated in (he policy is the amount actually paid if the specilied event oc- curs, regardless of whether an equivalent loss is actually suffered or not. With most forms of insurance of property the situation is different. W'liatcvcr may be the fare of the policy, the indcnuiity is not expected to exceed the loss ac- tually experienced. If insured property is par- tially destroyed and the loss does not exceed the amount of the insurance, the amount of loss fixes the maximum amount to be paid as indem- nity. In some countries in fire insurance any person who insures his property for less than its full value is licld to be his own insurer for the difference between the value of the property and the amount of the insurance; and if the prop- erty is partially destroyed, and the loss does not exceed the insurance, the indemnity actually paid is such part of the loss as the total amount 'of insurance in force is of the total value of the property. If, for example, property insured for three-fourths of its value is partially destroyed, the indemnity actually paid will be three-fourths of the loss. The rest of the loss will fall upon the insured as co-insurer. In the United States this principle is not commonly applied except in marine insurance. In {reneral. when insured property is partially destroyed and the loss does not exceed the amount of the insurance, the in- surance company becomes responsible for the entire amount of the loss. AVhen the loss fixes the maximum amount of indemnity, it is clear that the amount stated in the face of the policy cannot be taken as the measure of the real liability which a company assumes in insuring a piece of property. It is true that there is an abstract possibility that every time a loss occurs it will be large enough to call for the full amount of the insurance; but there is a practical certainty that in many cases loss and indemnity will be less than the face of the policy. It is necessary, therefore, to calcu- late what is the probable ratio of the indemnity to the amount of insurance, or. in other words, to estimate the probable intensity of the loss. This can be ascertained, not by a study of the char- acteristics of the insured property, but only by the statistical analysis of the results of past ex- perience. If it were shown by such analysis that for any particular kind of property the in- demnity in a large number of cases had been on the average one-half the amount stated in the face of the policy, then the amount the insurance company would actually have at stake in a policy issued on property of that kind would be one-half the amount stated in the face of the policy. Degree of Prohahilit;/. — The determination of the probability of the occurrence of the event against whose economic consequences insurance is granted is a much more complex matter than the determination of the amount which the in- surance company has at stake on a given policy. It is evident that this probability will vary with the lenffth of time for which the insurance is to be in force; that, other things being equal, the probability of the occurrence of a chance event is twice as great for two years as for one year. It will be convenient to approach the problem by leaving out of con>idiratiun the element of time and assuming that all insurance is granted for a uniform period, say for one year. We may then consider what changes, if any. the introduc- tion of the time element will involve. It is to l>e noted in the first place that it is impossible to determine the degree of probability by the most exhaustive study of the individual risk. It is easy to see that there is more danger in one case than another; that, for example, other things being equal, a wooden house is more likely to be burned than a stone house, but what the absolute probability is in either case dues not appear. Whether either will be destroyed or not is a matter of chance, though with different degrees of probability. By this it is not meant that the destruction is uncaused, but that the forces at work are so complex that human knowl- edge is incapable of analyzing them completely. As it is impossible to determine the degree of probability directly, the attempt is made to discover it in an indirect way. The method ia the application of the theory of probability to the statistical results of past experience. The average of the past is the probability of the fu- ture. If the records show that for a series of years an event has occurred 10 times a year for every 10.000 opportunities for its occurrence, th'e degree of probability that it will occur in a fu- ture year, conditions remaining unchanged, is denoted by the fraction 10/10.000, or 1/1000. The actual number of occurrences in any one year may vary more or less from the probable number as indicated by the average. The prob- able degree of this variation may be determined from the character of the past series. The greater the fluctuations in the series in the past, the greater the variations of actual from average that may be expected in the future. But what- ever the character of the past series, it will always be true that increasing the number of opportunities, provided they are all alike, dimin- ishes the probable variation of the actual num- ber of occurrences in any future year from the probable number as determined by past experi- ences. To state the same principle in a form nvv directly applicable to insurance, the greater the number of similar risks incliulcd in a group, the smaller the percentage of variation between the average number of losses for a s<Ties of years, and the actual number of losses for any particular year. The influence of time on probability under these ideally simplified conditions, that is, on the hypothesis that all circumstances affecting the degree of danger remain unchanged, is very simple. The probability varies directly in pro- portion to the time. For n years the probability is ji times as great as for one year. If. then, we represent by o the amount which an insurance company has at stake on a given policy, by p the probability of the occurrence of a loss within one year, and by n the number of years for which the company issues its policy, we should have the annual risk assumed by the company represented by the formula a X /), and the total risk for the n years represented by a X p X »i. The real difficulties involved in the attempt to estimate risk have not yet been touched upon. They are practical rather than theoretical. The determination of future events by the applica-
