On Risk Assessment and a Value Function under Extreme Uncertainty Based on the Concept of Regular Risk Structure

Abstract

This paper deals with how to describe one's preference on risk and a value function under extreme uncertainty. When we describe the degree of ignorance and uncertainty by basic probability of Dempster-Shafer theory, the problem is how to represent the value of the set element which consists of multiple elements. We propose a method of assessing preference on risk by taking into account the average value and the variance of the value of the multiple elements. Our method is based on the concept of Regular Risk Structure. Although it has been defined under known probability distribution, our method can be used under unknown probability distribution.