Głębokie sieci neuronowe w identyfikacji rozkładów brzegowych i wielowymiarowej kopuli w kontekście agregacji ryzyka w solvency II
Deep neural networks in identifying marginal distributions and multidimensional copula in the context of risk aggregation in Solvency II

Summary/Abstract: One of the basic aspects of the Solvency II Directive is the protection of the insured against the insol- vency of insurance companies. For this purpose, by aggregating the Solvency Capital Requirements for individual types of risk, the Solvency Capital Requirement (SCR) and the diversification effect (DE) are determined. The SCR may be determined using the Standard Formula (SF) given by the authors of the Directive is based on the variance-covariance (V-C) method or using internal models developed independently (by the companies). The aim of our present research is to use copulas estimated with the use of neural networks in modeling dependencies in the premium and reserve risk submodule. Two neural networks are constructed: the first to boundary distributions and the second to estimate the cop- ula. In the research, we analyze indicators for the segments of non-life insurers, determined from reports on the solvency and financial condition of Polish insurance companies. We compare the DE obtained by the V-C method, Vine copula and copula estimation approach using neural networks. The conduct- ed research indicates significant differences in the DE obtained for the copula estimated with the use of neural networks, parametric copula and the approach proposed by the authors of the Directive based on the V-C method. The obtained results can be used in internal models.

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