Optimal Insurance Strategy for Target Functional of Markowitz Type

This study solves the problem of finding the optimal risk sharing between the insurer and the client. A similar problem is often raised in the mathematical theory of insurance and represents an important applied task. The study was carried out using the static insurance model for the insurance theory and suggested finding an insurance strategy that would satisfy both the insured and the insurer. The total amount of work is 29 pages, 5 literary sources were mentioned in the work, for illustration of the results 6 figures were given and 8 tables were indicated. The introduction described the results of the analysis of articles that have made a great contribution to the development of the mathematical theory of insurance. In the theoretical part, the basic terms, definitions, and designations of the mathematical theory of insurance were described, the description of the model under study was also given, and optimality criteria were shown, which we guided our decision. The analytical part shows the course of the decision, the results of the study and a numerical example is given. The assumption was confirmed that the optimal risk sharing has the type of insurance with an upper limit (stop-loss insurance). The findings and results may be used in applied insurance problems.