Risk Quantization by Magnitude and Propensity

We propose a novel approach in the assessment of random risk variable X by introducing magnitude-propensity measures (mX, pX). This bivariate measure intends to account for dual aspect risk, where magnitudes x tell how high are losses incurred, whereas probabilities P(X = x) reveal often one has expect suffer such losses. The basic idea is simultaneously quantify both severity mX and propensity pX real-valued X. be contrasted with traditional univariate measures, like VaR or Expected shortfall, which typically conflate effects. In its simplest form, p X) obtained mass transportation Wasserstein metric law PX two-points {0,mX} discrete distribution at mX. can also formulated as constrained optimal quantization problem. This allows an informative comparison risks on magnitude scales. Several examples illustrate proposed approach.