Sharp convex bounds on the aggregate sums--An alternative proof
Abstract
It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32, 71-80. Cheung (2010), Characterizing a comonotonic random vector by the distribution of the sum of its components, Insurance: Mathematics and Economics 47(2), 130-136] and that a random vector with given marginal distributions is mutually exclusive if and only if it has the minimal convex sum [Cheung and Lo (2014), Characterizing mutual exclusivity as the strongest negative multivariate dependence structure, Insurance: Mathematics and Economics 55, 180-190]. In this note, we give a new proof of this two results using the theories of distortion risk measure and expected utility.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.05373
- arXiv:
- arXiv:1603.05373
- Bibcode:
- 2016arXiv160305373Y
- Keywords:
-
- Quantitative Finance - Risk Management
- E-Print:
- 11pages