The conditional higher moment risk measure for extreme risks

Abstract

Consider a risk position X whose performance is influenced by a certain risk factor Y, a situation that calls for conditional risk measurement. We propose the conditional higher moment risk measure, which provides a flexible framework for risk assessment by incorporating a given scenario for Y, a confidence level, and the decision-maker's risk aversion. We conduct an extreme value analysis of this risk measure to quantify how an extreme scenario of Y exacerbates the risk position of X. This analysis yields several asymptotic estimators, for which we establish asymptotic consistency and validate them via simulation studies. Finally, we conduct empirical studies to examine the impact of precip..