Derivatives Pricing in Incomplete Markets

In the paper the one-period (B, S) - market model with two securities is considered. In the introduction a replicating portfolio for the derivative security is obtained when the securities are primitive. In the second part we consider the situation where the stock price could have more than two values. We build an approximation of such a market using a fictive (B, S*) - market where the stock price could take only two values. In the third part the numerical illustration of the approximation is given

Frequency Instability Measurement Device Based on the Pulse Coincidence Principle

Актуальнiсть. Завдання швидкого й точного вимiрювання динамiчних характеристик сучасних джерел сигналiв з частотним виходом, зокрема функцiї короткочасної нестабiльностi частоти (ФКНЧ), потребує вдосконалення методiв вимiрювання з урахуванням необхiдностi полiпшення їх метрологiчних характеристик, зниження часу проведення випробувань, можливостi автоматизацiї вимiрювань за рахунок застосування iнформацiйно-вимiрювальних систем. Мета роботи полягає в розробцi методу вимiрювання ФКНЧ на принципi збiгiв iмпульсiв пакетами та експериментальних дослiдженнях вимiрювачiв на його основi. Метод. Розроблено метод вимiрювання функцiї короткочасної нестабiльностi частоти на принципi збiгiв регулярних незалежних послiдовностей iмпульсiв пакетами. Розроблений метод має переваги в порiвняннi з кращим варiантом методу на базi перетворення перiодчасовий iнтервал-код при роботi з однаковим початковим значенням дослiджуваної частоти i при роботi з однаковим значенням iнтервалу усереднення. Результати. Отриманi аналiтичнi спiввiдношення для основних метрологiчних характеристик. Проведено порiвняльний аналiз метрологiчних характеристик розробленого методу й методу на базi перетворення перiод-часовий iнтервал-код. Добрими метрологiчними характеристиками володiє метод вимiрювання ФКНЧ на базi перетворення перiод-часовий iнтервал-код, в якому формується вимiрювальний iнтервал як рiзниця дослiджуваного i опорного iнтервалiв i заповнюється iмпульсами дослiджуваної або опорної частот. Висновки. Реалiзовано автономний й вiртуальний вимiрювачi, а також проведено експериментальнi дослiдження стандартних генераторiв. Вказано особливостi вимiрювачiв i шляхи їх подальшого удосконалення. Подальший розвиток вимiрювача можливий в напрямку збiльшення кiлькостi вимiрюваних параметрiв джерел сигналiв з частотним виходом, зокрема, змiни короткочасної нестабiльностi частоти вiд впливу дестабiлiзуючих факторiв, характеристики i часу встановлення частоти. Для цього необхiдно розробити керований джерело дестабiлiзуючих факторiв i синхронiзувати його роботу з вимiрником.Context. The task of rapid and accurate measurement of the dynamic characteristics of modern signal sources with a frequency output, in particular, the short-time frequency instability function, calls for refining measurement techniques with account of the requirement to improve their metrological characteristics, reduce test time, and automate measurements by using information-and-measurement systems. Objective. The goal of the work is to develop a method of measuring the short-time frequency instability function using the principle of pulse packet coincidence and experimental investigation of measurement devices based on this principle. Method. A method was developed for measuring the short-time frequency instability function based on the principle of packet coincidence of regular independent pulse trains. The developed method has advantages over the best version of the method based on the period-time interval-code (PTC) conversion when working with the same initial value of the investigated frequency and when working with the same value of the averaging interval. Results. Analytical relationships were obtained for basic metrological characteristics. A comparative analysis was carried out for the metrological characteristics of the developed method and the method using period-time interval-code conversion. Acceptable metrological characteristics are inherent to the short-time frequency instability function (SFIF) measurement method based on the period-time interval-code technique. The difference of investigated and reference intervals form the measurement interval, which is filled with pulses of the investigated or reference frequencies. Conclusions. Stand-alone and virtual measurement devices were developed, and experimental studies of standard oscillators were carried out. The features of measurement devices were specified and the ways of their further improvement were described. Further development of the measurement device can involve an increase in the number of measured signal source with frequency output (SFO) parameters, in particular, changes in short-time frequency instability due to the action of destabilizing factors, and the characteristics and time of frequency setting. This calls for developing a controlled source of destabilizing factors and synchronizing its operation with the measurement device.Задача быстрого и точного измерения динамических характеристик современных источников сигналов с частотным выходом (ИЧВ), в частности функции кратковременной нестабильности частоты (ФКНЧ), требует усовершенствования методов измерения с учетом необходимости улучшения их метрологических характеристик, снижения времени проведения испытаний, возможности автоматизации измерений за счет применения информационно-измерительных систем. Цель работы состоит в разработке метода измерения ФКНЧ на принципе совпадения импульсов пакетами и экспериментальных исследованиях измерителей на его основе. Разработан метод измерения функции кратковременной нестабильности частоты на принципе совпадений регулярных независимых последовательностей импульсов пакетами. Разработанный метод имеет преимущества в сравнении с лучшим вариантом метода на базе преобразования ПВК при работе с одинаковым начальным значением исследуемой частоты и при работе с одинаковым значением интервала усреднения. Получены аналитические соотношения для основных метрологических характеристик. Проведен сравнительный анализ метрологических характеристик разработанного метода и метода на базе преобразования период-временной интервал-код. Хорошими метрологическими характеристиками обладает метод измерения ФКНЧ на базе преобразования период-временной интервал-код (ПВК), в котором формируется измерительный интервал как разность исследуемого и опорного интервалов и заполняется импульсами исследуемой или опорной частот. Реализованы автономный и виртуальный измерители, а также проведены экспериментальные исследования стандартных генераторов. Указаны особенности измерителей и пути их дальнейшего совершенствования. Дальнейшее развитие измерителя возможно в направлении увеличения количества измеряемых параметров ИЧВ, в частности, изменения кратковременной нестабильности частоты от воздействия дестабилизирующих факторов, характеристики и времени установления частоты. Для этого необходимо разработать управляемый источник дестабилизирующих факторов и синхронизировать его работу с измерителем

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil

Positronium laser cooling via the 13S1^3S-23P2^3P transition with a broadband laser pulse

We report on laser cooling of a large fraction of positronium (Ps) in free-flight by strongly saturating the $1^3S$-$2^3P$ transition with a broadband, long-pulsed 243 nm alexandrite laser. The ground state Ps cloud is produced in a magnetic and electric field-free environment. We observe two different laser-induced effects. The first effect is an increase in the number of atoms in the ground state after the time Ps has spent in the long-lived $3^3P$ states. The second effect is the one-dimensional Doppler cooling of Ps, reducing the cloud's temperature from 380(20) K to 170(20) K. We demonstrate a 58(9) % increase in the coldest fraction of the Ps ensemble.Comment: 6 pages, 5 figure

Influence of the ocean surface temperature and sea ice concentration on regional climate changes in Eurasia in recent decades

Numerical experiments with the ECHAM5 atmospheric general circulation model have been performed in order to simulate the influence of changes in the ocean surface temperature (OST) and sea ice concentration (SIC) on climate characteristics in regions of Eurasia. The sensitivity of winter and summer climates to OST and SIC variations in 1998-2006 has been investigated and compared to those in 1968-1976. These two intervals correspond to the maximum and minimum of the Atlantic Long-Period Oscillation (ALO) index. Apart from the experiments on changes in the OST and SIC global fields, the experiments on OST anomalies only in the North Atlantic and SIC anomalies in the Arctic for the specified periods have been analyzed. It is established that temperature variations in Western Europe are explained by OST and SIC variations fairly well, whereas the warmings in Eastern Europe and Western Siberia, according to model experiments, are substantially (by a factor of 2-3) smaller than according to observational data. Winter changes in the temperature regime in continental regions are controlled mainly by atmospheric circulation anomalies. The model, on the whole, reproduces the empirical structure of changes in the winter field of surface pressure, in particular, the pressure decrease in the Caspian region; however, it substantially (approximately by three times) underestimates the range of changes. Summer temperature variations in the model are characterized by a higher statistical significance than winter ones. The analysis of the sensitivity of the climate in Western Europe to SIC variations alone in the Arctic is an important result of the experiments performed. It is established that the SIC decrease and a strong warming over the Barents Sea in the winter period leads to a cooling over vast regions of the northern part of Eurasia and increases the probability of anomalously cold January months by two times and more (for regions in Western Siberia). This effect is caused by the formation of the increased-pressure region with a center over the southern boundary of the Barents Sea during the SIC decrease and an anomalous advection of cold air masses from the northeast. This result indicates that, to estimate the ALO actions (as well as other long-scale climatic variability modes) on the climate of Eurasia, it is basically important to take into account (or correctly reproduce) Arctic sea ice changes in experiments with climatic models

Диагностика инвазивного рака мочевого пузыря по лабораторным показателям с использованием статистических решающих правил

Based on studies of a wide spectrum of physicochemical parameters of the blood in 160 patients with vesical cancer, the authors created complexes of informative tests and formulated the decision rules fit for evaluating the degree of tumor invasion before therapy. The diagnostic efficiency of this approach amounts to 87.5—89%.

Improved functionalization of oleic acid-coated iron oxide nanoparticles for biomedical applications

Superparamagnetic iron oxide nanoparticles can providemultiple benefits for biomedical applications in aqueous environments such asmagnetic separation or magnetic resonance imaging. To increase the colloidal stability and allow subsequent reactions, the introduction of hydrophilic functional groups onto the particles’ surface is essential. During this process, the original coating is exchanged by preferably covalently bonded ligands such as trialkoxysilanes. The duration of the silane exchange reaction, which commonly takes more than 24 h, is an important drawback for this approach. In this paper, we present a novel method, which introduces ultrasonication as an energy source to dramatically accelerate this process, resulting in high-quality waterdispersible nanoparticles around 10 nmin size. To prove the generic character, different functional groups were introduced on the surface including polyethylene glycol chains, carboxylic acid, amine, and thiol groups. Their colloidal stability in various aqueous buffer solutions as well as human plasma and serum was investigated to allow implementation in biomedical and sensing applications.status: publishe

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.