Preprint Article Version 1 NOT YET PEER-REVIEWED

The Solvency II Standard Formula, Linear Geometry, and Diversification

Version 1 : Received: 10 October 2016 / Approved: 10 October 2016 / Online: 10 October 2016 (11:53:00 CEST)
Version 2 : Received: 28 February 2017 / Approved: 1 March 2017 / Online: 1 March 2017 (08:53:59 CET)

How to cite: Paulusch, J. The Solvency II Standard Formula, Linear Geometry, and Diversification. Preprints 2016, 2016100031 (doi: 10.20944/preprints201610.0031.v1). Paulusch, J. The Solvency II Standard Formula, Linear Geometry, and Diversification. Preprints 2016, 2016100031 (doi: 10.20944/preprints201610.0031.v1).

Abstract

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.

Subject Areas

Solvency II; standard formula; risk measure; diversification; aggregation; monotony; homogeneity; subadditivity; Euler’s principle; capital allocation

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