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山西师范大学学报（自然科学版） 2010年第S2期24卷 63-65页

作者：朱双杰 School of Chemistry and Life Science Chuzhou University

Specialized optional courses serve the purpose of perfecting knowledge structure,improving students quality,promoting the development of individual *** article discusses the embarassment of the specialized optional courses from the point of view of understanding the courses,programing of the courses,students' pressure,teachers' background knowledge and examing system first,then offers some counter-measures from the point of view of strengthen attitude,necessary interference,teaching methods,flexible examing system and strict examing system.

关键词： specialized optional courses teaching effect cause analysis counter-measure

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Assessment of Contingent Liabilities for Risk Assets Evolutions Built on Brownian Motion

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Advances in Pure Mathematics 2020年第5期10卷 259-296页

作者： Nicholas Simon Gonchar Bogolyubov Institute for Theoretical Physics of NAS of Ukraine Kyiv Ukraine

This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk assets, the important class of the random processes is the random processes with parameters built on the basis of the discrete geometric Brownian motion. For this class of random processes the interval of non-arbitrage prices are found for the wide class of contingent liabilities. In particular, for the payoff functions of standard options call and put of the European type the fair prices of super-hedge are obtained. Analogous results are obtained for the put and call of arithmetical options of Asian type. For the parameters entering in the definition of random process the description of all statistical estimates is presented. Statistical estimate for which the fair price of super-hedge for the payoff functions of standard call and put options of European type is minimal is indicated. From the formulas found it follows that the fair price of super-hedge can be less than the price of the underlying asset. In terms of estimates the simple formula for the fair price of super-hedge is found. Every estimates can be realized in the reality. This depends on the distribution function of the observed dates in the financial market.

关键词： Random Process Regular Set of Measures optional Doob Decomposition Local Regular Super-Martingale Martingale Assessment of Derivatives

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Description of Incomplete Financial Markets for Time Evolution of Risk Assets

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Advances in Pure Mathematics 2019年第6期9卷 567-610页

作者： Nicholas S. Gonchar Bogolyubov Institute for Theoretical Physics of NAS Kiev Ukraine

In the paper, a class of discrete evolutions of risk assets having the memory is considered. For such evolutions the description of all martingale measures is presented. It is proved that every martingale measure is an integral on the set of extreme points relative to some measure on it. For such a set of evolutions of risk assets, the contraction of the set of martingale measures on the filtration is described and the representation for it is found. The inequality for the integrals from a nonnegative random value relative to the contraction of the set of martingale measure on the filtration which is dominated by one is obtained. Using these inequalities a new proof of the optional decomposition theorem for super-martingales is presented. The description of all local regular super-martingales relative to the regular set of measures is presented. The applications of the results obtained to mathematical finance are presented. In the case, as evolution of a risk asset is given by the discrete geometric Brownian motion, the financial market is incomplete and a new formula for the fair price of super-hedge is founded.

关键词： Random Process Regular Set of Measures optional Doob Decomposition Local Regular Super-Martingale Martingale Discrete Geometric Brownian Motion

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Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

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Advances in Pure Mathematics 2018年第4期8卷 428-462页

作者： Nicholas S. Gonchar Bogolyubov Institute for Theoretical Physics of NAS Kiev Ukraine

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

关键词： Random Process Convex Set of Equivalent Measures optional Doob Decomposition Local Regular Super-Martingale Martingale Fair Price of Contingent Claim

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阿尔泰语系语言数范畴的标记系统及其表义功能

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语言文字学 2022年第7期

作者：姚家兴

阿尔泰语系语言名词数范畴整体上呈现出单、复数对立的格局，人称代词具有绝对的数范畴区分，复数标记具有强制性，而名词的复数标记是非强制的，具有可选性，且受一定的句法、语义及语用因素的制约，动词的数范畴主要表示事件数及参与... 详细信息

阿尔泰语系语言名词数范畴整体上呈现出单、复数对立的格局，人称代词具有绝对的数范畴区分，复数标记具有强制性，而名词的复数标记是非强制的，具有可选性，且受一定的句法、语义及语用因素的制约，动词的数范畴主要表示事件数及参与者人数，部分形容词及量词的数范畴不具有普适性。除典型的黏着性形态标记外，阿尔泰语系语言还可通过句法手段、词汇手段以及重叠手段等表达数范畴意义，不同词类在数范畴的编码形式上存在较大差异，同一词类内部的不同成员也可选用不同的语法手段编码数范畴意义。名词复数标记除表达真性复数的核心功能语义外，还具有丰富的扩展性功能。整体上来看，阿尔泰语系语言数范畴标记系统符合语言类型学上的诸多共性特征，一些黏着形态标记的表义功能具有较为凸显的个性特点。

关键词：阿尔泰语系语言数范畴编码形式可选性表义功能 Altaic languages number expression optional meaning function

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