Guaranteed solution for risk-neutral decision maker: an analog of maximin in single-criterion choice problem

V. I. Zhukovskii^a, L. V. Zhukovskaya^b, Yu. S. Mukhina^a, S. P. Samsonov<sup>a

a</sup> Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Optimal Control Leninskiye Gory, GSP-1, Moscow, 119991, Russia
^b Federal State Budgetary Institution of Science Central Economic and Mathematical Institute of the Russian Academy of Sciences (CEMI RAS), Nakhimovskii prosp., 47, Moscow, 117418, Russia

Abstract: In this article single-criterion choice problems under uncertainty (SCPUs) are considered. The principle of minimax regret and the Savage-Niehans risk function are introduced. A possible approach to solving an SCPU for a decision-maker who simultaneously seeks to increase his outcome and reduce his risk (“to kill two birds with one stone”) is proposed. The explicit form of such a solution for the linear-quadratic setup of the SCPU is obtained.

Keywords: guaranteed solution, single-criterion choice, Savage-Niehans risk, minimax regret, uncertainties.

UDC: 517.577.1

MSC: 91A10

Language: English