Joint identifiability/elicitability of JMES with other risk measures

Determine whether the Joint Marginal Expected Shortfall JMES_{α,β}, when combined with other risk measures such as Value-at-Risk, admits a strict identification function or a strictly consistent scoring function (i.e., is jointly identifiable or jointly elicitable) on appropriate classes of bivariate distributions, thereby enabling traditional or comparative backtesting of the joint vector of risk measures.

Background

The authors prove that JMES_{α,β} is neither identifiable nor elicitable on classes containing all bivariate normal distributions and their finite mixtures, implying JMES alone cannot be backtested in the standard frameworks of traditional or comparative backtesting.

They suggest that joint consideration with other risk measures might restore identifiability or elicitability. The open task is to establish whether suitable joint functionals involving JMES (e.g., pairing with VaR) admit strict identification functions or strictly consistent scoring functions, and on what distribution classes.