Guaranteed decision for risk-neutrality: the analogue of maximin in one-criterion problem

V. I. Zhukovskii ; S. N. Sachkov ; E. N. Sachkova

Taurida Journal of Computer Science Theory and Mathematics, no. 3 (2018), pp. 46-70

Résumé

In the middle of the last century, the American mathematician and statistician Professor of the University of Michigan Leonard Savage (1917–1971) and the famous Swiss economist, Professor of the University of Zurich Jurg Niehans (1919–2007) independently proposed an approach to the choice of the solution in the one-criterion problem under uncertainty (OPU), called the principle of minimax regret (according to Niehans–Savage). This principle, along with the Wald's principle of guaranteed result (maximin), plays a crucial role in making a guaranteed decision in OPU. The main role in the principle of minimax regret is the function of regret, which determines the risk according to the Niehans–Savage in the OPU. This risk has been widely used in practical management tasks in recent years. In this article, one of the possible approaches to finding a solution in OPU «from the position» of risk-neutrality — the person making the decision, who simultaneously tries to improve its gain (outcome) and reduce the risk («to kill two birds with one stone with one shot ») is proposed. As an application, the explicit form of such solution is found for a linear-quadratic variant of the OPU in general form.

Détail

Keywords: strategy, uncertainty, gain, function of risk, risk according to the Niehans-Savage, the principle of minimax regret.