In the socialist countries, where insurance — like the other primary sectors of the national economy — has been nationalized and is conducted by a single state-owned insurance company, a whole number of actuarial problems have arisen. These are problems which either did not interest the private insurance companies or else were marginal questions for them, of no great practical importance. The actuarial problems which have cropped up or have acquired particular importance in the conditions of socialist economy, include questions connected with evaluation of the efficiency of outlays for the insurance company's preventive activities intended to restrict the number and scope of chance damages). Henceforth we shall refer to expenditures of this sort as preventive outlays /expenditures/.

One of the initial problems pertaining to the preventive activities of the state insurance monopoly is one which could be called the optimum structure of the trends of activities to prevent chance damages.

We present the problem in the most simple form, formulating it so that it can be solved by generally-known calculus methods employed in linear programming (e.g. the simplex method given by G. B. Danzig in 1951).

Let us assume that in a given period, e.g. in a year, the insurance company allocates a certain sum I for preventive purposes. Realization of these outlays is expected to reduce damage payments made by the insurance company during that period; let us call that decrease Q, the „savings” obtained by the insurance company.