Analysis and formulation of mathematical models for decision-making in stochastic and uncertain environment. For a discrete models of stochastic optimization proved the convergence of the solutions of the corresponding discrete problem of optimization
on time series and obtained estimates for optimal objective values. Applications of the Best Guaranteed Result Principle to operations with stochastic factors. Proved theorems showing that the best-guaranteed result in the operation can be determined as a solution to a certain optimization problem.
For a two-level hierarchical control systems, where conflict-reducing roles are assigned to the upper level and conflict-intensifying functions to lower ones, analyzed a framework for revising degrees of freedom and proved the existence of the Pareto-optimal solutions.
Analysis and implementation of Computerized Decision-Support Systems. Analyzed technique for valuing of contingent claims and developed computer applications for options pricing.
