Wald–Savage optimality principle for mixed strategies and the financial application

Subject. This article considers the process of making optimal decisions under conditions of uncertainty, based on the Wald–Savage principle for mixed strategies. Objectives. The article aims to find a structure of the set of strategies that are optimal in a set of mixed strategies according to the Wald–Savage criterion, provided that there is a strategy in the game that is optimal in a set of mixed strategies according to both the Wald criterion and the Savage criterion, and apply the result obtained in solving the problem of financial and economic content. Methods. For the study, we used the methods and facts from the theory of games with nature, probability theory, finite-dimensional Euclidean spaces, and multidimensional mathematical analysis. Results. The article proves a theorem that describes the structure of a set of strategies that are optimal in a set of mixed strategies according to the Wald-Savage criterion, provided that a strategy exists in the game that is optimal in a set of mixed strategies according to both the Wald criterion and the Savage criterion. The application of the results obtained is illustrated through solving the problem of optimal distribution of funds intended for the purchase of shares of two issuers. Conclusions and Relevance. The results obtained represent a new approach to the optimal allocation of funds intended for investments in various fields, and therefore have practical significance. From a scientific and theoretical point of view, the results make a definite contribution to the development of the theory of games with nature. The results obtained can be applied in various fields of science and practice in making optimal decisions under conditions of uncertainty.