How Superadditive Can a Risk Measure Be?

Wang, R., Bignozzi, V. & Tsanakas, A. (2015). How Superadditive Can a Risk Measure Be?. SIAM Journal on Financial Mathematics, 6(1), pp. 776-803. doi: 10.1137/140981046

[img]
Preview
Text - Accepted Version
Download (749kB) | Preview

Abstract

In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure, by yielding the worst-possible diversification ratio across dependence structures. One of the main contributions is demonstrating that, for a wide range of risk measures, the extreme-aggregation measure corresponds to the smallest dominating coherent risk measure. In our main result, it is shown that the extremeaggregation measure induced by a distortion risk measure is a coherent distortion risk measure. In the case of convex risk measures, a general robust representation of coherent extreme-aggregation measures is provided. In particular, the extreme-aggregation measure induced by a convex shortfall risk measure is a coherent expectile. These results show that, in the presence of dependence uncertainty, quantification of a coherent risk measure is often necessary, an observation that lends further support to the use of coherent risk measures in portfolio risk management.

Item Type: Article
Additional Information: Copyright Society for Industrial and Applied Mathematics 2015
Uncontrolled Keywords: distortion risk measures; shortfall risk measures; expectiles; dependence uncertainty; risk aggregation; diversification
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/12693

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics