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2013 | 1 | 54-64
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Are law-invariant risk functions concave on distributions?

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
While it is reasonable to assume that convex combinations on the level of random variables lead to a reduction of risk (diversification effect), this is no more true on the level of distributions. In the latter case, taking convex combinations corresponds to adding a risk factor. Hence, whereas asking for convexity of risk functions defined on random variables makes sense, convexity is not a good property to require on risk functions defined on distributions. In this paper we study the interplay between convexity of law-invariant risk functions on random variables and convexity/concavity of their counterparts on distributions. We show that, given a law-invariant convex risk measure, on the level of distributions, if at all, concavity holds true. In particular, this is always the case under the additional assumption of comonotonicity.
Wydawca
Czasopismo
Rocznik
Tom
1
Strony
54-64
Opis fizyczny
Daty
otrzymano
2013-10-04
zaakceptowano
2013-12-07
online
2013-12-17
Twórcy
Bibliografia
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  • [14] R. Kaas and J. Dhaene and D. Vyncke and M.J. Goovaerts and M. Denuit. A simple geometric proof that comonotonicrisks have the convex-largest sum. Astin Bull. 32/1, 71-80, (2002).[Crossref]
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_demo-2013-0003
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