In the present work we analyse the dynamics of indirect connections between insurance companies that result from market price channels. In our analysis we assume that the stock quotations of insurance companies reflect market sentiments which constitute a very important systemic risk factor. Interlinkages between insurers and their dynamics have a direct impact on systemic risk contagion in the insurance sector. We propose herein a new hybrid approach to the analysis of interlinkages dynamics based on combining the copula-DCC-GARCH model and Minimum Spanning Trees (MST). Using the copula-DCC-GARCH model we determine the tail dependence coefficients. Then, for each analysed period we construct MST based on these coefficients. The dynamics is analysed by means of time series of selected topological indicators of the MSTs in the years 2005-2019. Our empirical results show the usefulness of the proposed approach to the analysis of systemic risk in the insurance sector. The times series obtained from the proposed hybrid approach reflect the phenomena occurring on the market. The analysed MST topological indicators can be considered as systemic risk predictors.

This work is a response to the EIOPA paper entitled 'Systemic risk and macroprudential policy in insurance', which asserts that in order to evaluate the potential systemic risk (SR), the build-up of risk, especially risk arising over time, should be taken into account, as well as the interlinkages occurring in the financial sector and the whole economy. The topological indices of minimum spanning trees (MST) and the deltaCoVaR measure are the main tools used to analyse the systemic risk dynamics in the European insurance sector in the years 2005-2019. The article analyses the contribution of each of the 28 largest European insurance companies, including those appearing on the G-SIIs list, to systemic risk. Moreover, the paper aims to determine whether the most important contribution to systemic risk is made by companies with the highest betweenness centrality or the highest degree in the obtained MST.

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We study the elliptic inclusion given in the following divergence formAs we assume that f ∈ L 1 (Ω), the solutions to the above problem are understood in the renormalized sense. We also assume nonstandard, possibly nonpolynomial, heterogeneous and anisotropic growth and coercivity conditions on the maximally monotone multifunction A which necessitates the use of the nonseparable and nonreflexive Musielak-Orlicz spaces. We prove the existence and uniqueness of the renormalized solution as well as, under additional assumptions on the problem data, its relation to the weak solution. The key difficulty, the lack of a Carathéodory selection of the maximally monotone multifunction is overcome with the use of the Minty transform. CONTENTS 1. Introduction 2. N -functions and Musielak-Orlicz spaces 3. Main results 4. Multivalued term and its regularization 5. Proof of Theorem 3.6: existence. 6. Proof of Theorem 3.7: uniqueness. 7. Proof of Theorem 3.12: relation between renormalized and weak solution. References Appendix

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We are looking for tools to identify, model, and measure systemic risk in the insurance sector. To this aim, we investigated the possibilities of using the Dynamic Time Warping (DTW) algorithm in two ways. The first way of using DTW is to assess the suitability of the Minimum Spanning Trees’ (MST) topological indicators, which were constructed based on the tail dependence coefficients determined by the copula-DCC-GARCH model in order to establish the links between insurance companies in the context of potential shock contagion. The second way consists of using the DTW algorithm to group institutions by the similarity of their contribution to systemic risk, as expressed by DeltaCoVaR, in the periods distinguished. For the crises and the normal states identified during the period 2005–2019 in Europe, we analyzed the similarity of the time series of the topological indicators of MST, constructed for 38 European insurance institutions. The results obtained confirm the effectiveness of MST topological indicators for systemic risk identification and the evaluation of indirect links between insurance institutions.