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Are law-invariant risk functions concave on distributions?

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Acciaio B., Svindland G.

Dependence Modeling

2013

tom 1

54-64

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.

Ograniczanie wyników

1 Dependence Modeling

1 Acciaio B.

1 Svindland G.

1 2013

Wyniki wyszukiwania

Are law-invariant risk functions concave on distributions?