C02 - Mathematical MethodsReturn

The contribution deals with the risk regulation in the framework of Solvency II, which is the new regulatory system in insurance valid in majority of the EU countries since 2016. It concentrates on the underwriting risk (in particular, on the reserve risk) and on the counterparty default risk (i.e. mainly on the reinsurers' default risk), since such risks are crucial for insurance activities. Various actuarial approaches to the underwriting risk applied by subjects respected by insurance regulators and supervisors are surveyed. Moreover, one of them suggests by means of a real data example a simplified approach to the reserve risk, which may be appreciated in practice just for its simplicity. As to the counterparty default risk, the paper presents a method that can be suitable when the reinsurers form a small group of heterogeneous subjects imperilled by a common shock as a financial crisis or a natural catastrophe; this methodological approach is also demonstrated by a numerical example.

We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters' theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the BaxterKing filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough.

The paper describes the changes in Czech economy in the period between 1970 and 2010 from the macroeconomic perspective. It is based on the detailed study of sources and uses of gross domestic product with respect to labour inputs. Used data sources come from recently published historical data on GDP combined with the data of oicial statistics. The paper should provide an analysis of the main determinants of growth based on output and expenditure approach to GDP and employment including the industrial analysis of labour productivity. In this paper labour productivity is estimated as the ratio of gross value added in the constant prices over the input used. As we have the data of total employment in full time equivalent we used them as the only possible labour input for the productivity analysis for the period in question.

Municipalities with extended administration, in which public administration offices are located, were selected within the frame of public administration reform (Act No. 344/1997 Coll., on the Territorial Arrangement of the State and Establishment of Higher Territorial & Administrative Units). These municipalities with extended administration partly substitute the function of district authorities. The selection of municipalities was carried out on the basis of criteria set by the government and political subjects. From the point of view of citizens, the most important criterion for the dislocation of public administration branch offices is the transport availability. Nevertheless, transport availability was not paid relevant attention in the decision making process in question. This fact becomes more and more important in connection with the growing problems related to ensuring regional transport. The paper deals with the creation of a mathematical model of the optimisation of branch offices dislocation and subsequent implementation. The solution of this model has three outputs. The first output is the evaluation of the contemporary state from the point of view of accessibility of branch offices. The second one is the sensibility analysis of accessibility depending on the number of branch offices. The third output is the post-optimisation analysis, which brought about numerical expression of the relationship between the cost of running a branch office and losses due to citizens travelling to municipalities with extended administration.

The paper deals with the approximation problem of standard growth accounting method first introduced by Solow (1957). This method is still used widely by lots of economists and institutions (IMF, national banks and others) for computing the technological or total factor productivity (TFP) dynamics. According to standard growth accounting the TFP growth is a residual, computed simply out of dynamic Cobb-Douglas (original or modified) production function. The purpose of this paper is to show that the usual TFP calculation as a residual is more or less inaccurate and for certain cases can cause slightly biased conclusions. The idea of such weak approximation is based on the nature of differential itself. The growth accounting computes the TFP dynamics accurately only under certain conditions based mainly on assumption of sufficiently small changes in variables.