Are law-invariant risk functions concave on distributions?

• Autorzy: Beatrice Acciaio , Gregor Svindland
• 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.

Słowa kluczowe

EN

convexity; law-invariant risk measure; convex order; comonotonicity

Kategorie tematyczne

• 46N10: Applications in optimization, convex analysis, mathematical programming, economics
• 60E15: Inequalities; stochastic orderings
• 91B30: Risk theory, insurance

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2013
• Tom: 1
• Strony: 54-64

Daty

otrzymano

2013-10-04

zaakceptowano

2013-12-07

online

2013-12-17

Twórcy

autor

Beatrice Acciaio

• The London School of Economics and Political Science

autor

Gregor Svindland

• University of Munich

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Identyfikatory

DOI

10.2478/demo-2013-0003