Dispersion Theory of Risk : Characteristics and a Comparative Study of Five Models

Risk and uncertainty in decisions play an important role in many fields including engineering, economics and social sciences. In order to represent the decision problem mathematically or to compare prospects, a scalar either as dispersion measure or risk measure is used. Adequately measuring dispersion or risk is one of the most challenging topics in decision theory. According to well-known definitions in the literature, a dispersion or risk measure should satisfy several good properties; non-negativity, monotonicity, and convexity. In this paper, we investigate properties of two dispersion measures of Geometric Dispersion Theory (GDT) which are based on arithmetic-geometric means and show that they are nonnegative and convex. Also, these new dispersion measures of GDT are less sensitive to noise in comparison to standard deviation and its generalizations. Furthermore, we show that these new measures can present riskiness of alternatives better than other measures; thus enabling GDT to explain several well-known decision-making paradoxes