Conditional risk based on multivariate hazard scenarios

We present a novel methodology to compute conditional risk measures when the conditioning event depends on a number of random variables. Specifically, given a random vector (X,Y), we consider risk measures that express the risk of Y given that X assumes values in an extreme multidimensional region. In particular, the considered risky regions are related to the AND, OR, Kendall and Survival Kendall hazard scenarios that are commonly used in environmental literature. Several closed formulas are considered (especially in the AND and OR scenarios). An application to spatial risk analysis involving real data is discussed.