Characterizing a comonotonic random vector by the distribution of the sum of its components
In this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures.
Year of publication: |
2010
|
---|---|
Authors: | Cheung, Ka Chun |
Published in: |
Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 47.2010, 2, p. 130-136
|
Publisher: |
Elsevier |
Keywords: | Convex order Stop-loss order Comonotonicity Distortion risk measure Distortion function |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Tail Mutual Exclusivity and Tail-Var Lower Bounds
Cheung, Ka Chun, (2015)
-
Upper comonotonicity and convex upper bounds for sums of random variables
Dong, Jing, (2010)
-
Comonotonic convex upper bound and majorization
Cheung, Ka Chun, (2010)
- More ...