arXiv subjects

Anna Denkowska

Publications and source records attributed to Anna Denkowska.

10 recordsLinked to original sources

arXiv2022

The Kuratowski convergence of medial axes and conflict sets

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold $\mathcal{M}$ under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.

math.MG↗

arXiv2020

Development and similarity of insurance markets of European Union countries after the enlargement in 2004

The enlargement of the European Union to new countries in 2004 launched mechanisms supporting the development of various social and economic areas, as well as levelling the differences between the Community members in these areas. This article focuses on the insurance sector. Its main purpose is to analyze the development and similarity of the insurance markets of old and new members of the European Union after the enlargement in 2004.

q-fin.ST↗

arXiv2020

On renormalized solutions to elliptic inclusions with nonstandard growth

We study the elliptic inclusion given in the following divergence form \begin{align*} & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad Ω, & u=0\quad \mathrm{on}\quad \partial Ω. \end{align*} As we assume that $f\in L^1(Ω)$, 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.

math.AP↗

arXiv2020

A tail dependence-based MST and their topological indicators in modelling systemic risk in the European insurance sector

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.

q-fin.ST↗

arXiv2019

A Dynamic MST- deltaCovar Model Of Systemic Risk In The European Insurance Sector

This work is an answer to the EIOPA 2017 report. It follows from the latter that in order to assess the potential systemic risk we should take into account the build-up of risk and in particular the risk that arises in time, as well as the interlinkages in the financial sector and the whole economy. Our main tools used to analyse the systemic risk dynamics in the European insurance sector during the years 2005-2019 are the topological indices of minimum spanning trees (MST) and the deltaCoVaR measure. We address the following questions: 1) What is the contribution to systemic risk of each of the 28 largest European insurance companies whose list includes also those appearing on the G-SIIs list? 2) Does the analysis of the deltaCoVaR of those 28 insurance companies and the conclusions we draw agree with the our claims from our latest article [Wanat S., Denkowska A. 2019]. In clear: does the most important contribution to systemic risk come from the companies that have the highest betweenness centrality or the highest degree in the MST obtained?

q-fin.GN↗

arXiv2019

Linkages and systemic risk in the European insurance sector: Some new evidence based on dynamic spanning trees

This paper is part of the research on the interlinkages between insurers and their contribution to systemic risk on the insurance market. Its main purpose is to present the results of the analysis of linkage dynamics and systemic risk in the European insurance sector which are obtained using correlation networks. These networks are based on dynamic dependence structures modelled using a copula. Then, we determine minimum spanning trees (MST). Finally, the linkage dynamics is described by means of selected topological network measures.

q-fin.ST↗

arXiv2019

Dependencies and systemic risk in the European insurance sector: Some new evidence based on copula-DCC-GARCH model and selected clustering methods

The subject of the present article is the study of correlations between large insurance companies and their contribution to systemic risk in the insurance sector. Our main goal is to analyze the conditional structure of the correlation on the European insurance market and to compare systemic risk in different regimes of this market. These regimes are identified by monitoring the weekly rates of returns of eight of the largest insurers (five from Europe and the biggest insurers from the USA, Canada and China) during the period January 2005 to December 2018. To this aim we use statistical clustering methods for time units (weeks) to which we assigned the conditional variances obtained from the estimated copula-DCC-GARCH model. The advantage of such an approach is that there is no need to assume a priori a number of market regimes, since this number has been identified by means of clustering quality validation. In each of the identified market regimes we determined the commonly now used CoVaR systemic risk measure. From the performed analysis we conclude that all the considered insurance companies are positively correlated and this correlation is stronger in times of turbulences on global markets which shows an increased exposure of the European insurance sector to systemic risk during crisis. Moreover, in times of turbulences on global markets the value level of the CoVaR systemic risk index is much higher than in "normal conditions".

econ.GN↗

arXiv2018

The Bernstein-Walsh-Siciak Theorem for analytic hypersurfaces

As a first step towards a general set-theoretic counterpart of the remarkable Bernstein-Walsh-Siciak Theorem concerning the rapidity of polynomial approximation of a holomorphic function on polynomially convex compact sets in $\mathbb{C}^n$, we prove a version of this theorem for analytic hypersurfaces.

math.CV↗

arXiv2018

UPC condition with parameter for subanalytic sets

In 1986 Pawłucki and Pleśniak introduced the notion of {\sl uniformly polynomially cuspidal} (UPC) sets and proved that every relatively compact and fat subanalytic subset of ${\Rz}^n$ satisfies the UPC condition. Herein we investigate the UPC property of the sections of a relatively compact open subanalytic set $E\subset{\Rz}^k\times{\Rz}^n$ and we show that two of the three parameters in the UPC condition can be chosen independently of the section, while the third one depends generally on the point defining the section.

math.MG↗

arXiv2018

Linear programming on non-compact polytopes and the Kuratowski convergence with application in economics

The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it together with an economical interpretation. Then, we turn to considering a dynamic version of the linear programming problem in that we consider the Kuratowski convergence of polyhedra and study the behaviour of optimal solutions. Our methods are purely geometric.

math.OC↗