Optimal insurance strategy in the individual risk model under a stochastic constraint on the value of the final capital

The article is devoted to solving a problem of the choice of an optimal insurance policy in a static model with the goal functional of Markowitz type. Constraint on an upper value of insurer's risk and a value at risk constraint are imposed. A normal distribution is used for modeling the distribution of summary insurer's risk. The optimal insurance policy turrns out to be a stop loss insurance. Conditions of the refuse of the insurance deal are found in an explicit form. An example illustrating the theoretical results in the case of an exponential distribution of claim size is given.