Dynamic Model of Insurance Company's Management

In this paper, we are interested in a model related to a number of periods of Company's activity.The Company calculates an amount s which then could be given as a supplementary interest to the shareholders. This calculated amount is taken from the risk reserve. Let us assume the risk reserve = S at the beginning of an operating period. If the Company gives an amount s to the shareholders, then the risk reserve is S — s. (Borch 1972; Seal 1969).We must determine the best policy of dividends, that is a rule which determines the payments to be made each year to the shareholders of the Company, maximising a definite criterion.The problem of dividends must be approached in the “dynamic programming manner”. Indeed, the payments of dividends have an effect upon further gains of the Company and its capacity to pay dividends in the future.The objective of the Company is, for example, maximising the average utility of the dividend payments, which is calculated according to the distribution of claims. (Borch 1964a; Wolff 1966).