Risk Quantization by Magnitude and Propensity

05/27/2021
by   Olivier P. Faugeras, et al.
0

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

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset