The Solvency II Standard Formula, Linear Geometry, and Diversification
Keyword(s):
Lp Norm
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We introduce the notions of monotony, subadditivity, and homogeneity for functions defined on a convex cone, call functions with these properties diversification functions and obtain the respective properties for the risk aggregation given by such a function. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Any Lp norm has this property, and any scalar product given by a non-negative positive semidefinite matrix as well. In particular, the Standard Formula is a diversification function, hence a risk measure that preserves homogeneity, subadditivity, and convexity.
2017 ◽
Vol 10
(2)
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pp. 11
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Keyword(s):
2017 ◽
Vol 21
(4)
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pp. 552-564
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