Pathwise integration with respect to paths of finite quadratic variation

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise 'signal plus noise' decomposition for regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation.Comment: To appear in: Journal de Mathematiques Pures et Appliquee

Rough differential equations with path-dependent coefficients

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives

Excursion Risk

The risk and return profiles of a broad class of dynamic trading strategies, including pairs trading and other statistical arbitrage strategies, may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies, based on a description in terms of price excursions, first in a pathwise setting, without probabilistic assumptions, then in a Markovian setting. We introduce the notion of delta-excursion, defined as a path which deviates by delta from a reference level before returning to this level. We show that every continuous path has a unique decomposition into delta-excursions, which is useful for the scenario analysis of dynamic trading strategies, leading to simple expressions for the number of trades, realized profit, maximum loss and drawdown. As delta is decreased to zero, properties of this decomposition relate to the local time of the path. When the underlying asset follows a Markov process, we combine these results with Ito's excursion theory to obtain a tractable decomposition of the process as a concatenation of independent delta-excursions, whose distribution is described in terms of Ito's excursion measure. We provide analytical results for linear diffusions and give new examples of stochastic processes for flexible and tractable modeling of excursions. Finally, we describe a non-parametric scenario simulation method for generating paths whose excursion properties match those observed in empirical data.Comment: 36 pages; 10 figure

PRINCIPAL DIRECTIONS OF EXTRABUDGETARY FUNDS IN HIGHER VOCATIONAL EDUCATION SYSTEM

The efforts of state higher educational institutions to attract extrabudgetary funds are analyzed. The analysis of the current problems, sources and prospects of income from the independent statutory activity is made

Rough differential equations with path-dependent coefficients

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives

Pathwise integration with respect to paths of finite quadratic variation

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation

Digital economy, the development ways of cryptocurrency

The article is devoted to new directions of development of the digital economy. The analysis of technology development and cryptocurrency blokcheyn. Analyzed the problems and prospects of transition to digital economy technology

Pathwise Integration and functional calculus for paths with finite quadratic variation

This thesis develops a pathwise calculus for non-anticipative functionals of paths with finite quadratic variation and studies its relation with the theory of controlled paths. We study the mathematical properties of a pathwise integral defined as a limit of Riemann sums for a class of non-anticipative gradient-type integrands. We establish for this integral a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals, and obtain a pathwise 'signal plus noise' decomposition as a unique sum of a pathwise integral and a component with zero quadratic variation for regular functionals of an irregular path with non-vanishing quadratic variation. Our results are strictly pathwise but apply to typical paths of continuous semimartingales. In the second part of the thesis we explore the relations between this non-anticipative functional calculus and the theory of controlled paths. We show that a regular functional generates a family of controlled paths whose `Gubinelli derivative' may be represented as a directional derivative. Conversely, we show that a family of controlled paths parameterized by the underlying control function may be represented as a vertically differentiable functional. This result leads to a chain rule for controlled paths and systematic way of constructing them. In the last part of the thesis we extend these results to functionals of discontinuous paths which are right-continuous with left limits.Open Acces

GENERAL APPROACHES AND WESTERN EXPERIENCE IN MANAGING AND FINANCING UNIVERSITY EDUCATIONAL PROCESSES

The most important financial economic models of governing and funding the university educational processes are considered. The approaches based on three models – when funding is provided either by the state, or by private investors, or on the mixed principle – are described. The Western experience based on the Anglo-Saxon and Continental models is analyzed. The comparative analysis of the key features of the Russian and Western universities is presented