Ruin probability for generalized φ-sub-Gaussian fractional Brownian motion

In this paper we investigate the ruin problem for the generalized φ-sub-Gaussian fractional Brownian motion (FBM). Such random process has the same covariation function as FBM but its trajectories belong to the space of φ-sub-Gaussian random variables (i.e. not necessarily Gaussian). For this risk process we obtain estimate of the ruin probability

Random process from the class V(φ,ψ): exceeding a curve

Random processes from the class V (φ, ψ) which is more general than the class of ψ-sub-Gaussian random process. The upper estimate of the probability that a random process from the class V (φ, ψ) exceeds some function is obtained. The results are applied to generalized process of fractional Brownian motion

Systems of financial analysts training

A review of different systems of financial analysts training which exist in European countries and the United States of America is proposed. MBA diploma and professional qualification such as Chartered Financial Analyst designation (CFA) in the United States of America, or Certified International Investment Analyst designation (CIIA) in Europe and Asia, are required for financial analysts to get certain level within a firm. We consider in details qualification levels that are offered by the most famous institutions such as Faculty of Actuaries and Institute of Actuaries (UK), Chartered Financial Analyst Institute (USA), Association of Certified International Investment Analysts, Association of Corporate Treasurers (UK). In Ukraine an equivalent international qualification can be obtained in the Training Center for Actuaries and Financial Analysts

Alternative estimate of curve exceeding probability of sub-Gaussian random process

Investigation of sub-gaussian random processes are of special interest since obtained results can be applied to Gaussian processes. In this article the properties of trajectories of a sub-Gaussian process drifted by a curve a studied. The following functionals of extremal type from stochastic process are studied: $\sup_{t\in B}(X(t)-f(t))$, $\inf{t\in B}(X(t)-f(t))$ and $\sup_{t\in B}|X(t)-f(t)|$. An alternative estimate of exceeding by sub-Gaussian process a level, given by a continuous linear curve is obtained.  The research is based on the results obtained in the work \cite{yamnenko_vasylyk_TSP_2007}. The results can be applied to such problems of queuing theory and financial mathematics as an estimation of buffer overflow probability and bankruptcy probability.Key words: sub-Gaussian process, metric entropy, supremum distribution, trajectory of random process.Pages of the article in the issue: 37 - 39Language of the article: Englis

Differentiation of Methods and Means of Protection of Patients ‘Rights in Ukraine

Забезпечення прав та свобод людини, її честі та гідності є головними чинниками становлення та розвитку суспільства. Так, в умовах демократизації українського суспільства особливої гостроти набуває питання забезпечення та захист прав, свобод та законних інтересів громадян. А одним із основних немайнових прав особи є право на здоров’я. Сьогодні Україна вступає в період створення нової системи охорони здоров’я – системи, що ґрунтується на потребах населення, тобто скерованої на пацієнта, на повагу до його прав, реалізацію основних положень захисту.Today, Ukraine is entering a period of creating a new health care system - a system based on the needs of the population, ie aimed at the patient, respect for his rights, the implementation of basic protection provisions. The proclamation by the Constitution of Ukraine of a person, his life, honor and dignity, inviolability and security as the highest social value determines the duty of the state not only to guarantee, but also to actually ensure the inalienable and inviolable rights of citizens to health care. The concept of the patient and his legal status are clarified; the rights of the patient in Ukraine are characterized. The main ways and means of protecting their rights are considered. However, the issue of their actual provision and compliance is one of the most problematic and requires immediate solution through the improvement of existing and introduction of new mechanisms for their protection, able to quickly and effectively address important legal issues of patients caused by ignorance, non-compliance, noncompliance or direct violation. medical care, state-prescribed legal regulations designed to protect the rights of patients

Оцінювання ймовірності виходу траєкторії строго φ\varphi-субгауссового процесу квазідробового ефекту за криву

In this paper, we continue to study the properties of a separable strictly φ-sub-Gaussian quasi shot noise process $X(t) = \int_{-\infty}^{+\infty} g(t,u) d\xi(u),  t\in\R$, generated by the response function g and the strictly φ-sub-Gaussian process ξ = (ξ(t), t ∈ R) with uncorrelated increments, such that E(ξ(t)−ξ(s))^2 = t−s, t>s ∈ R. We consider the problem of estimating the probability of exceeding some level by such a process on the interval [a;b], a,b ∈ R. The level is given by a continuous function f = {f(t), t ∈ [a;b]}, which satisfies some given conditions. In order to solve this problem, we apply the theorems obtained for random processes from a class V (φ, ψ), which generalizes the class of φ-sub-Gaussian processes. As a result, several estimates for probability of exceeding the curve f by sample pathes of a separable strictly φ-sub-Gaussian quasi shot noise process are obtained. Such estimates can be used in the study of shot noise processes that arise in the problems of financial mathematics, telecommunication networks theory, and other applications.Key words: shot noise processes, φ-sub-Gaussian processes.Pages of the article in the issue: 49 - 56Language of the article: UkrainianУ роботі  досліджуються властивості строго $\varphi$-субгауссового процесу квазідробового ефекту $X(t)=\int_{-\infty}^{+\infty}g(t,u)d\xi(u),$ $t\in\R$, породженого випадковим процесом $\xi$ та функцією відгуку~$g$. Отримано оцінки для ймовірності виходу траєкторії строго $\varphi$-субгауссового процесу квазідробового ефекту за криву

Professor Yu.V. Kozachenko (01.12.1940 - 05.05.2020) - prominent scientist and teacher

Pages of the article in the issue: 9 - 29Language of the article: Ukrainia

ORGANIZING COMMITEE

Присвячена 60-рiччю кафедри теорiї ймовiрностей i математичної статистики та пам’ятi М.Й.Ядренка (1932-2004) МАТЕРIАЛИ КОНФЕРЕНЦIЇ 19-23 червня, 200