Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: http://hdl.handle.net/10419/178591
Autoren: 
Paulusch, Joachim
Datum: 
2017
Quellenangabe: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 10 [Year:] 2017 [Issue:] 2 [Pages:] 1-12
Zusammenfassung: 
The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence, Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each Lp norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity and convexity.
Schlagwörter: 
Solvency II
standard formula
risk measure
diversification
aggregation
monotony
homogeneity
subadditivity
Euler's Principle
capital allocation
Persistent Identifier der Erstveröffentlichung: 
Creative-Commons-Lizenz: 
https://creativecommons.org/licenses/by/4.0/
Dokumentart: 
Article

Datei(en):
Datei
Größe
254.18 kB





Publikationen in EconStor sind urheberrechtlich geschützt.