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## Воспроизводимость условных квантилей многомерных распределений и упрощенная конструкция из парных копул

We give an equivalent definition of the conditional quantile reproducibility property for multivariate probability distributions using the concept of copula. Based on this definition, we establish a connection between the conditional quantile reproducibility property and the simplifying assumption from the simplified pair copula construction. Additionally, we show that the conditional quantile reproducibility is preserved when moving from a multivariate distribution to its copula.

The objective of the research is to study the properties of joint distribution of returns for dry bulk time charter rates and to find out the more efficient time series model describing their dynamics with respect to goodness-of-forecasting.

In this paper, we introduce a principally new method for modelling the dependence structure between two L{\'e}vy processes. The proposed method is based on some special properties of the time-changed Levy processes and can be viewed as an reasonable alternative to the copula approach.

This paper proposes method of detecting a structural break/shift in time series such as AR(1) with a nonlinear dependence structure of lagged value and the estimation of the break point, based on nonparametric estimations of the dependence’s copulas and comparison with some existing tests. However, we assumed the time series to be stationary and homoscedastic. This paper compares the efficiency of the standard test, considering only linear autoregressive dependence nature. A suggested technique is given, some modifications of the evaluation scheme is offered and a more flexible method of detecting structural break is proposed, usefulness of our methodology is demonstrated through some applications to a few macroeconomic and financial time series. The paper is organized as follows: the first section contains a selective literature review. The second section describes the generation’s procedure of time series, used in further calculations. The problem of detection of the structural break with respect to the nonlinear time series is formulated in the third section. The fourth section contains results of evaluations using simulated data. In Sect. 5 we provide examples of our suggested technique. The final section contains "Conclusions".

The article deals with the issue of copula use in the program of price risk hedging. Copula-models performance is compared to the OLS-based ones. Fully parametric and semi-parametric approaches to copula-modeling are compared. The copula-based models efficiency is illustrated by the fact of decreasing the daily profit-and-loss volatility of the hedged portfolio by simultaneously augmenting its total yield compared to the OLS-based hedge ratio computation during the back-testing period. Nevertheless, it is shown that copula-based approaches are able to outperform OLS-based ones only for direct hedging programs, while for cross-hedging ones OLS do better.

According to the strategy of the banking system development until 2015, the Central Bank of Russia is going to implement Basel II Internal-Ratings-Based (IRB) approaches in 2015, while Basel III is planned to be introduced in full starting from 2019. Taking into account the effects of the Basel II regulation during the crisis 2008-2009, in particular, the excessive procyclicality of the capital requirements, it is important to investigate the consequences of its adoption for the stability of the banking system in Russia.

The aim of this paper is to model the Russian banking system capital adequacy under the Basel II IRB approach. The main hypothesis tested refers to the existence of the procyclicality effect of the capital adequacy for the whole banking system as if Basel II has been introduced. The research is based on publicly available quarterly financial statements of all the Russian banks for the period 2004Q1-2010Q1. Copulas are used to model joint banking risks distribution.

The methodology consists of three steps. First of all, the copula structural shift for the joint risk distribution for the Russian banking system is assessed in order to examine the dynamics of the individual risks’ dependence and analyze the change in the level of the banking system stability. Secondly, risk-weighted assets are modelled using copula. Finally, the Value-at-Risk approach is employed to arrive at the capital adequacy ratio for the Russian banking system.

The analysis of the copula structural shift shows the downward change in the risks’ interconnection starting from the third quarter of 2005 being associated with the increased stability of the banking system. Basel II capital adequacy ratio fell to the minimum of 4% during the period 2009-2010, while the Basel I capital adequacy ratio was well above 15%. However, the hypothesis of the procyclical nature of Basel II is rejected.

The research undertaken highlights the necessity for further investigation and calibration of the models proposed in Basel II and Basel III. Moreover, it is important to work out the appropriate policy options with respect to banks bearing high risks under Basel II.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.