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Distortion Risk Measures for Sums of Random Variables
| Content Provider | Semantic Scholar |
|---|---|
| Author | Darkiewicz, Grzegorz Dhaene, Jan Goovaerts, Marc J. |
| Copyright Year | 2004 |
| Abstract | where FX(t) denotes the distribution function of X ≥ 0. The distortion risk measures have some useful properties, e.g. positive homogeneity, translation invariance, additivity for comonotonic risks, preservation of stochastic dominance. Moreover if one additionally assumes concavity of the distortion function g than the corresponding risk measure will be also subadditive. These properties of distortion risk measures have been comprehensively studied in many works (see e.g. Wang (1996), Wang et. al (1998), Wang and Young (1998), Wirch and Hardy (2000), Dhaene et. al (2004)). In this contribution we investigate the behavior of distortion risk measures when applied to sums of random variables against some well-known dependency measures between summands (we assume that the marginal distributions are fixed). The theorem we cite below states that when the dependency level differs strongly (which is expressed in the terms of the so-called correlation order of pairs of random variables) and the distortion function is concave (which implies the aversion towards risk well-known from the utility theory), then the corresponding risk measure should behave consistently with increasing dependence between the variates in the sum, and increase. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.econ.kuleuven.ac.be/tew/academic/actuawet/pdfs/Distortion2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Biologic Preservation Concave function Distortion Marginal model Risk aversion Risk measure Utility emotional dependency |
| Content Type | Text |
| Resource Type | Article |
