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. Preprints2016, 2016100031. https://doi.org/10.20944/preprints201610.0031.v1
Paulusch, J. The Solvency II Standard Formula, Linear Geometry, and Diversification. Preprints 2016, 2016100031. https://doi.org/10.20944/preprints201610.0031.v1
Paulusch, J. The Solvency II Standard Formula, Linear Geometry, and Diversification. Preprints2016, 2016100031. https://doi.org/10.20944/preprints201610.0031.v1
APA Style
Paulusch, J. (2016). The Solvency II Standard Formula, Linear Geometry, and Diversification. Preprints. https://doi.org/10.20944/preprints201610.0031.v1
Chicago/Turabian Style
Paulusch, J. 2016 "The Solvency II Standard Formula, Linear Geometry, and Diversification" Preprints. https://doi.org/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.
Keywords
Solvency II; standard formula; risk measure; diversification; aggregation; monotony; homogeneity; subadditivity; Euler’s principle; capital allocation
Subject
Business, Economics and Management, Finance
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
