Kirilyuk V. Optimal decisions in risk conditions on the basis of technique of set-valued maps.

The theory and methods for optimal decision making in risk conditions were developed. The class of polyhedral coherent risk measures was studied, and portfolio optimization problems for return-risk ratio were reduced to appropriate linear programming problems. Different portfolio optimization problems, in particular, under unknown scenarios probabilities, multi-objective statements. Optimization problems for parallel-series systems with failures of both types and their generalizations were researched, effective algorithms for solution searching were designed. Technique of set-valued maps is developed: a new tangent cone for graphs was designed, and new results for different properties of set-valued maps were obtained. Approach of nonparametric estimating systems on input-output was disseminated to systems with risks.