Ordering and Inequalities for Mixtures on Risk Aggregation

Ordering and Inequalities for Mixtures on Risk Aggregation

Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this talk, we investigate ordering relations between two aggregation sets for which the sets of marginals are related by two simple operations: distribution mixtures and quantile mixtures. Intuitively, these operations ``homogenize" marginal distributions by making them similar.

As a general conclusion from our results, more ``homogeneous" marginals lead to a larger aggregation set, and thus more severe model uncertainty, although the situation for quantile mixtures is much more complicated than that for distribution mixtures. We proceed to study inequalities on the worst-case values of risk measures in risk aggregation, which represent conservative calculation of regulatory capital. Among other results, we obtain an order relation on VaR under quantile mixture for marginal distributions with monotone densities. Numerical results are presented to visualize the theoretical results and further inspire some conjectures. Finally, we discuss the connection of our results to joint mixability and to merging p-values in multiple hypothesis testing.

Speaker

Peng Liu, University of Essex

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Osama Mahmoud (o.mahmoud@essex.ac.uk).