Insurance Regulation and Life Catastrophe Risk: Treatment of Life Catastrophe Risk Under the SCR Standard Formula of Solvency II and the Necessity of Partial Internal Models

2014 ◽  
Vol 40 (2) ◽  
pp. 256-278 ◽  
Author(s):  
Gunther Kraut ◽  
Andreas Richter
Keyword(s):  
Solvency Ii ◽  
Internal Models ◽  
Insurance Regulation ◽  
Catastrophe Risk ◽  
Standard Formula ◽  
Risk Treatment

FUNDAMENTAL DEFINITION OF THE SOLVENCY CAPITAL REQUIREMENT IN SOLVENCY II

2014 ◽  
Vol 44 (3) ◽  
pp. 501-533 ◽  
Author(s):  
Marcus C. Christiansen ◽  
Andreas Niemeyer
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Solvency Ii ◽  
Capital Requirement ◽  
Insurance Regulation ◽  
Modeling Framework ◽  
Solvency Capital Requirement ◽  
Risk Margin ◽  
Solvency Capital ◽  
Definition Of

AbstractIt is essential for insurance regulation to have a clear picture of the risk measures that are used. We compare different mathematical interpretations of the Solvency Capital Requirement (SCR) definition from Solvency II that can be found in the literature. We introduce a mathematical modeling framework that enables us to make a mathematically rigorous comparison. The paper shows similarities, differences, and properties such as convergence of the different SCR interpretations. Moreover, we generalize the SCR definition to future points in time based on a generalization of the value at risk. This allows for a sound definition of the Risk Margin. Our study helps to make the Solvency II insurance regulation more consistent.

scholarly journals The Solvency II Standard Formula, Linear Geometry, and Diversification

2016 ◽  
Author(s):  
Joachim Paulusch
Keyword(s):  
Convex Cone ◽  
Risk Measure ◽  
Positive Semidefinite ◽  
Solvency Ii ◽  
Positive Semidefinite Matrix ◽  
Lp Norm ◽  
Standard Formula ◽  
Risk Aggregation ◽  
Semidefinite Matrix ◽  
Linear Geometry

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.

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