JMES-based measures under CoD with two joint distress events

Develop JMES-based systemic risk measures within the Conditional Distortion (CoD) framework that condition on two joint distress events generated by both risks X and Y, and analyze their theoretical properties and comparisons.

Background

The paper’s JMES conditions on simultaneous exceedances of X and Y at (possibly different) thresholds and is not, in general, a CoD measure. The authors suggest a further generalization: constructing JMES-type measures under the CoD framework while conditioning on two joint distress events induced by both X and Y.

Such a development would bridge JMES with the broader CoD class and provide systematic tools for modeling simultaneous stress events in systemic risk assessment.

References

Another interesting problem might be generalizing the JMES-based measures under the setting of CoD-risk measures by considering two joint distress events generated by $X$ and $Y$; see . We leave these interesting problems for future studies.

— On Joint Marginal Expected Shortfall and Associated Contribution Risk Measures  (2405.07549 - Pu et al., 2024) in Concluding remarks, Section 7