Research Repository

Ordering and Inequalities for Mixtures on Risk Aggregation

Chen, Yuyu and Liu, Peng and Liu, Yang and Wang, Ruodu (2022) 'Ordering and Inequalities for Mixtures on Risk Aggregation.' Mathematical Finance, 32 (1). pp. 421-451. ISSN 0960-1627

[img] Text
aggregationMF_revision_R1final.pdf - Accepted Version
Restricted to Repository staff only until 15 June 2023.

Download (643kB) | Request a copy


Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this paper, 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 provide applications on portfolio diversification under dependence uncertainty and merging p-values in multiple hypothesis testing, and discuss the connection of our results to joint mixability.

Item Type: Article
Uncontrolled Keywords: aggregation set; distribution mixture; quantile mixture; risk measure; joint mixability
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 01 Jul 2021 10:54
Last Modified: 22 Jan 2022 20:18

Actions (login required)

View Item View Item