Vine copulas and fuzzy inference to evaluate the solvency capital requirement of multivariate dependent risks

2021 ◽  
pp. 1-17
Author(s):  
Sawssen Araichi ◽  
Tarifa Almulhim
Keyword(s):  
Fuzzy Inference ◽  
Capital Requirement ◽  
Solvency Capital Requirement ◽  
Dependent Risks ◽  
Solvency Capital ◽  
Vine Copulas

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 TEST FOR CHANGES IN THE MODELED SOLVENCY CAPITAL REQUIREMENT OF AN INTERNAL RISK MODEL

2021 ◽  
pp. 1-25
Author(s):  
Daniel Gaigall
Keyword(s):  
Risk Model ◽  
Broad Class ◽  
Capital Requirement ◽  
Insurance Company ◽  
Model Output ◽  
The European Union ◽  
Finite Sample ◽  
Test Statistic ◽  
Solvency Capital Requirement ◽  
Solvency Capital

ABSTRACT In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

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