Generalized Kelly strategy

We study the possibility of influence on the saving of allocated funds for the elimination of consequences of natural disasters. At that, we take into account statistical data on the emergence of such phenomena and the degree of actual damage. The article describes the problem of determining the optimal share of funds that either replenish or spend the principal amount according to the distribution. We prove that, under certain conditions of the distribution and a positive mathematical expectation, it is possible to choose a share that ensures the maximum possible growth of the original deposit account. At the same time, the choice of the share allows not to lose the full provision of damage recovery. This process is presented as a serial multi-stage process based on a Markov chain that takes into account only the distribution based on the statistical data of this year to plan the size of the deposit share for the next year. For simplicity, we assume that the process is established and has a constant distribution for some time. The distribution table can be changed in the case of a major change in stochastic data. We consider a serial multi-stage process of changing the monetary amount that is purposefully deposited for the renewal, replacement and restoration of security and alarm systems at burned-out facilities. The optimal stochastic control of the change in the share of the money deposit providing this restoration is carried out based on the generalized Kelly formula. An example of model validity is shown. On the basis of statistical data, the analysis of the possibility to use this model is carried out.