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Optimal Dividend Strategy in Compound Binomial Model with Bounded Dividend Rates

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 859-870页

作者： Ji-yang TAN Xiang-qun yang School of Mathematics and Computational Science Xiangtan University College of Mathematics and Computer Science Hunan Normal University

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a *** company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.

关键词： compound binomial model optimal dividend strategy transformation

On a BMAP/G/1 G-queue with Setup Times and Multiple Vacations

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Acta Mathematicae Applicatae Sinica 2011年第4期27卷 625-638页

作者： Yi PENG Xiang-qun yang School of Mathematical Science and Computing Technology Central South University Changsha 410075 Hunan China College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China

In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.

关键词： G-queues batch Markovian arrival process (BMAP) setup times multiple vacations censoring technique Markov chains

Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 653-660页

作者： Luo-gen Yao Gang yang Xiang-qun yang Information Department of Hunan Business College Changsha 410205China College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081China

The Moore-Penrose inverse is an important tool in *** paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure *** extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still ***,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose ***,the minimal martingale measure in a generalized Black-Scholes model is found.

关键词： Moore-Penrose inverse minimal martingale measure semi-martingales structure condition

Unified Characteristic Numbers and Solutions of Equations for Birth and Death Processes with Barriers

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Acta Mathematicae Applicatae Sinica 2010年第3期26卷 443-454页

作者： Xiang-qun yang He-song Wang College of Mathematics and Computer Science Hunan Normal University. Changsha 410081 China College of Mathematics and Computer Science Changsha University of Science and Technology Changsha410076 China

The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds： reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.

关键词： birth and death process with barrier reflection and absorption leaping reflection andquasi-reflection characteristic numbers solutions of equations

Option Pricing by Mean Correcting Method for Non-Gaussian Lvy Processes

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Acta Mathematica Sinica,English Series 2013年第10期29卷 1927-1938页

作者： Luo Gen YAO Gang yang Xiang qun yang School of Mathematics and Statistics Hu'nan Business College College of Mathematics and Computer Science Hu'nan Normal University

For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivial, this pricing method may lead to arbitrage in some cases. In the latter case, some necessary and sufficient conditions under which option price is arbitrage-free are obtained.

关键词： Non-Gaussian Levy processes mean correcting method option pricing

Criterion of Semi-Markov Dependent Risk Model

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Acta Mathematica Sinica,English Series 2014年第7期30卷 1273-1280页

作者： Xiao Yun MO Xiang qun yang Department of Basic Subjects Hu’nan University of Finance and Economics College of Mathematics and Computer Science Hu’nan Normal University

A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.

关键词： Semi-Markov dependent risk model Markov dependent risk model criterion necessarycondition Markov chain

A Periodic Dividend Problem with Inconstant Barrier in Markovian Environment

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Acta Mathematica Sinica,English Series 2015年第2期31卷 281-294页

作者： Fang JIN Hui OU Xiang qun yang College of Mathematics and Computer Sciences Hu'nan Normal University

Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.

关键词： Periodic dividend Markovian environment inconstant barrier ruin time discounted dividends contraction mapping principle

Investigation of Formation Process of the Chrome-free Passivation Film of Electrodeposited Zinc

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Chinese Journal of Aeronautics 2007年第2期20卷 129-133页

作者： ZHU Li-qun yang Fei HUANG Hui-jie School of Materials Science and Engineering Beijing University of Aeronautics and Astronautics Beijing 100083 China

The feasibility was investigated to substitute chrome-free passivation treatment of electrodeposited zinc in a titanium bath for chromate passivation treatment. The formation mechanism of the chrome-free passivation film was further analyzed. The surface mor- phologies and the elemental compositions of the treated samples with varied immersion times were observed by scanning electron mi- croscopy （SEM） and determined by energy dispersion spectrometry （EDS）, respectively. The electrode potential of the sample surface was recorded in the film formation process. The changes of the electrode potential are in accordance with that of SEM and EDS of the sample surface. The results of X-ray photoelectron spectroscopy （XPS） show the chrome-free passivation film composed ofZnO, SiO2, TiO2, Zn4Si207（OH）2, and SrF2. The anode zinc dissolution and the local pH value increase due to the cathode hydrogen ion reduction process result in the formation of the chrome-free passivation film. The macro-images of the chrome-free passivation films formed on electrodeposited zinc show that the color of the film changes from blue to iridescence with the increase of the immersion times.

关键词： electrodeposited zinc chrome-free pasivation film film formation process

Structures of sodium vanadate solution under different conditions

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Rare Metals 2018年第1期37卷 59-65页

作者： Ya-Li Zhang Li-qun yang Xian-Jin Yu School of Chemical Engineering Shandong University of Technology

Combined with Fourier transform infrared spectroscopy（FTIR） analysis of sodium vanadate solution,the relationship between conductivity and structure was investigated by measuring the electric conductivity of the solution under different alkali concentrations and molar ratios of NaOH to V2O5. Results suggest that the polymerization vanadium acid radical ions gradually transform into monomer with the solution diluting. When the solution is diluted to a certain extent,only the vanadium acid radical ion with V-OH chemical bond exists in the solution. At NaOH concentration of below 105.21 g·L^（-1）,the vanadate anions mainly exist in the form of vanadium acid radical ion with V-OH chemical bond and the ion transference number is approximately from 0.58 to 0.82. In the medium NaOH concentration range of 105.21-117.03 g·L^（-1）, the vanadate anions mostly exist in the form of vanadium acid radical ion with V-OH and V-O-V chemical bonds and the ion transference number is approximately 3.29. At NaOH concentration of above 117.03 g·L^（-1）, vanadate anions exist in the form of vanadium acid radical ion with V-OH and V-O-V chemical bonds.

关键词： Sodium vanadate solution Electric conductivity Migration number Infrared spectroscopy