Frameworks for Comparison and Measurement of Risk

In this essay, we present an overview of the methods for comparison and quantification of risk. First, we review general frameworks for comparison of so called lotteries via ordinal preferences. The concept of replicating these preferences by (expected) utility functions is discussed. The attitude of risk-averseness is then explained in terms of the individuals’ utility functions. We then review stochastic dominance rules that provide a basis to compare different random variables (lotteries) in somewhat utility-invariant manner. In particular, it is shown that Second Order Stochastic Dominance (SSD) rules can be naturally utilized for comparing risks. Next, we discuss methods of quantifying risks via monetary risk measures. These measures are defined to be monotone and cash invariant. Convex measures are also considered to include the natural effect of diversification in reducing risks. Finally, some examples of risk measures and their interpretations are provided.