Risks in a Multicriteria Problem under Uncertainty

Applicability and novelty of the following research lies in that the decision-maker in a multicriteria problem aims not only to maximize guaranteed values of each criterion, but also to minimize the guaranteed risks accompanying the said maximization. The topic of the research lies at the interface of the multicriteria problem (MP) theory and the Savage–Nichans minimax regret principle (MRP): the concept of a weakly effective estimate has been derived from the MP theory, while estimation of risks with values of the Savage–Nichans regret function has been derived from the MRP. The scope of this research is limited to interval uncertainties: the decision-maker only knows the limits of the interval, and probabilistic characteristics are missing. A new term of a “strongly guaranteed solution under outcomes and risks” (SGSOR) is introduced; its existence for “regular”–confined–strategies for the mathematical programming is established. As an example of a practical application, a problem of diversification of a multi-currency deposit has been suggested and solved.

Keywords: Pareto maximum, strategy, uncertainty, vector guarantee, Savage risk, principle of minimax regret.