Determination of an insurance company non-bankruptcy terms in individual risk model

Abstract

Historical development studied of agrarian business risks insurance problem. Basic scientific and organizational attempts to solve it are shown as well as training standards of insurance specialists in Russian Empire of late XIX – early XX century. Information specified on educational institutions which existed at that period in Kyiv and Kharkiv to train respective officials. Authors assumed as a condition of successful insurance company operation at the above period of time the term that total company assets including insurance premium and own capital exceed the amount of insurance payments. The probability of insurance company bankruptcy avoidance was accepted as equal to the probability of the amount of insurance payments not exceeding the amount of its assets. For solution of this problem the individual risk model was used. The work dwells on the following approaches to solution of this problem: expected value principle and mean-square deviation principle. Expected value principle determines the value of insurance company assets necessary for its successful operation as a value equal to k-fold excess above average value of insurance payments. Mean-square deviation principle determines the value of insurance company assets necessary for its successful operation as a value equal to the sum of average value and r-fold value of insurance payments mean-square deviation. Solution of set problems was studied for such distribution laws: normal, lognormal, gamma distribution, Weibull distribution, inverse Gaussian distribution, Pareto distribution, Burr distribution type XII, Dagum distribution. Fragments of respective tables are added as necessary for practical usage by insurance officers.