On optimal planning of the reserve with applications to insurance. (Q5947823)

The equation for a reserve volume minimizing the average cost conditioned both by keeping a product during the given period and by shortage of the product is given. Supposing that the flow of requirements has a Poisson distribution two-sided estimates for a solution of the equation are found by use a normal approximation. Then the problem is generalized for the case when requirements are not obligatory positive. In this case the two-sided estimates may be used for finding the optimal value of an initial capital of an insurance company. A criterion of optimality bound both with a possibility of investments of the free capital in some profitable projects and with a possibility in some necessary cases to use credits.