The structure of the set of strategies, optimal in the set of mixed strategies according to the Wald–Savage criterion, and the financial application

Subject. The article considers a set of strategies that are optimal in the set of mixed strategies according to the Wald–Savage criterion with a win-rate ? ? [0,1]. Objectives. The aim is to find a structure of the set of strategies that are optimal in the set of mixed strategies according to the Wald–Savage criterion with a win rate, provided that there is no strategy in the game that is optimal in the set of mixed strategies according to both the Wald criterion and the Savage criterion; to apply the findings to solve financial and economic problems. Methods. We employ methods and facts from the theory of games with nature, the theory of infinite sets, mathematical analysis and plane geometry. Results. The study proves the theorem describing the structure of a set of strategies optimal in the set of mixed strategies according to the Wald–Savage criterion with a win rate, provided that there is no strategy optimal in the set of mixed strategies according to both the Wald criterion and the Savage criterion. The application of findings is illustrated by solving the problem of optimal distribution of funds intended for the acquisition of shares of two issuers. Conclusions. The findings represent a new approach to optimal distribution of funds intended for investments in various projects. They contribute to the development of the theory of games with nature, may be used when making optimal decisions under complete uncertainty. This also applies to the financial and economic sphere.