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2017, Vol. 37 No. 2   Published date: 30 June 2017
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• Controlled Bisexual Branching Processes

  Qiu Yumei, Hu Yangli, Peng Xuelian

  2017, 37(2): 1-10. doi:

  Abstract ( 1933 )   PDF (365KB) ( 404 )   　　

  In this paper we investigate the limiting behavior of superadditive controlled bisexual branching processes.The relation of the mean growth rate of mating units between a controlled bisexual branching process and a bisexual branching processes is obtained,and the limiting behaviors of sequences normalized respectively by the upper and lower bounds of the conditional mean value are studied.

• Properties of Quadratic Weighted Markov Branching Processes with Immigration and Resurrection

  Qu Shanshan, Wang Juan

  2017, 37(2): 11-17. doi:

  Abstract ( 1920 )   PDF (271KB) ( 501 )   　　

  In this paper we study the regularity,uniqueness,recurrence and ergodicity of the quadratic weighted Markov branching processes with immigration and resurrection(QWMBPIR).Firstly,we investigate the properties of the generating function for QWMBIR q-matrix.It is proved that the QWMBPIR is regular and unique.Then we discuss the recurrence and ergodicity of QWMBPIR and give a sufficient condition for the ergodicity.

• General Exchange Option Pricing in Sub-fractional Brownian Motion Environments

  Xu Feng

  2017, 37(2): 18-23. doi:

  Abstract ( 1947 )   PDF (235KB) ( 440 )   　　

  his paper studies the pricing problem of general exchange options in sub-fractional Brownian motion environments.Under the condition that the two stock pricing processes obey the stochastic differential equation driven by the sub-fractional Brownian motion,the pricing formula of the general exchange options is obtained by insurance actuary pricing.

• Stability Analysis of Solutions for a Class of Stochastic Difference Equations

  Ge Lingling, Liao Xinyuan, Chen Huili, Lu Yinxia

  2017, 37(2): 24-31. doi:

  Abstract ( 2083 )   PDF (386KB) ( 701 )   　　

  In this paper,asymptotic behavior of a class of linear stochastic difference equation is investigated.Using the discrete Itô formula and stochastic difference comparison theorem,we obtain the sufficient conditions for the stochastic stability and instability of this equation.Finally,under a simple condition,the correctness of the conclusion is showed by Matlab.

• Image Denoising Algorithm Based on Total Variation

  Ni Nianyong, Sun Bo

  2017, 37(2): 32-37. doi:

  Abstract ( 2168 )   PDF (564KB) ( 1119 )   　　

  In this paper we study the image denoising algorithm based on total variation.The corresponding optimization model is solved by the steepest descend method,the difference iterative method and the split Bregman method,respectively.Experiment results show that the difference iterative method convergences rapidly,and achieves better denoising performances.

• A Risk Model of Two Type Claims Under a Ruin Threshold

  Qin Lihua

  2017, 37(2): 38-47. doi:

  Abstract ( 1917 )   PDF (358KB) ( 482 )   　　

   In this paper,we study a risk model of two type claims under a time-dependent ruin bound,where one term policy’s arrival intensity follows a Poisson process of parameterλand its refunding,its abnormal claims and normal claims are respectively relate to the policies ofρ₁-thinning process,ρ₂-thinning process andρ₃ -thinning process,while the other term policy and claim arrival both follow the compound negative binomial distribution.For the risk model we investigate the properties of the surplus process by applying the martingale approach and derive the formula of ruin probability and the Lundberg inequality.

• Ruin Probability of a Dependent Risk Model with Generalized Polya-Aeppli Distribution

  Liu Yuanxun, Zhao Dianli

  2017, 37(2): 48-59. doi:

  Abstract ( 1988 )   PDF (441KB) ( 589 )   　　

  In this paper,we study the ruin probability of a risk model with two dependent compensation processes based on the generalized Polya-Aeppli distribution.Firstly,the joint probability distribution function and the precise expressions of moments for a class of dependent processes are derived by applying the probability generating function defined by Kocherlakota (1995).Then two kinds of ruin models are formulated,and the corresponding ruin probabilities are obtained by using the Laplace transformation to covert computing ruin probability to calculating probability distribution function of the cumulative claims when the claims follow the exponential distribution.The generalized Polya-Aeppli distribution defines a class of discrete distributions with correlation.It overcomes the over-dispersion problem of the actual data which cannot be modeled by Poisson process,and is easy to estimate the parameters.Thus our approach has a wide range of applicability.

• A New Cryptosystem Based on a Kind of Integer Matrix Equations

  Huang Xiantong, Gu Tianye, Yan Shenhai

  2017, 37(2): 60-64. doi:

  Abstract ( 1912 )   PDF (195KB) ( 523 )   　　

  In this paper a new cryptosystem is designed based on solving the unique solution to a kind of finite field integer matrix equations and the secret-sharing Differ-Hellman protocol.The validity and effectiveness are showed by a numerical example.

• Numerical Simulation of Heavy Metal Migration Process in Submarine Near Deep Sea Mining

  Xiao Guoguang, Guo Yongnan, Zhao Haitao, Hu Meijuan

  2017, 37(2): 65-72. doi:

  Abstract ( 2098 )   PDF (1478KB) ( 402 )   　　

  Based on the physical migration of the water phase and the siliceous nuclide,this paper analyzes the migration and diffusion,adsorption and suspension of the heavy metals near the deep sea mining vessel sedimentation. A global model and some phase separation models of heavy metal migration and transformation are established by making use of the equations of hydraulics and sediment dynamics.The models are solved by differential algorithms.Given the parameters in the models by experiments or measurements,the migration of heavy metals is then simulated by the MATLAB software with intuitive demonstration.

• Extension of the Wallis Formula and Stirling Formula

  Han Kai

  2017, 37(2): 73-78. doi:

  Abstract ( 2434 )   PDF (237KB) ( 1019 )   　　

  Wallis’formula and Stirling’s formula are two important formulas in advanced mathematics.In this paper we firstly extend these formulas to non-integer situation to yield a generic Wallis formula and a generic Stirling formula, and then investigate the relation between these formulas.

• Probability Properties of Order Statistics to Bilaterally Truncated Cauchy Distribution#br#

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  Xiong Xiong, Tuo Heng

  2017, 37(2): 79-87. doi:

  Abstract ( 2242 )   PDF (700KB) ( 426 )   　　

   Let {X_k,1≤k ≤n}be independent and identically distributed random variables with bilaterally truncated Cauchy distribution of parameters μ,λ,A,B,X_1,n,X_2,n,…,X_n,n be their order statistics.In this paper we obtain the density function of X_k,n,the joint density function of X_1,n,X_2,n,…,X_n,n,the asymptotic distributions of their extreme order statistics X_1,n and X_n,n,and the asymptotic distributions of X_k,n and X_n-k+1,n.We also show that X_1,n and X_n,n is asymptotically independent.

• Solving the Optimization Model of Equipment Preventive Maintenance Period with the Genetic Algorithm and Nonlinear Programming

  Huang Jian

  2017, 37(2): 88-96. doi:

  Abstract ( 1995 )   PDF (700KB) ( 667 )   　　

  By establishing the relationship between the failure rates before and after preventive maintenances, this paper gives a nonlinear constrained model of equipment preventive maintenance strategy.The model aims to minimize the total cost of the system in a finite production time interval by synthetically considering the repair cost,preventive maintenance cost and production loss cost.It is solved by making use of the global search ability of genetic algorithm and the local search ability of nonlinear programming.A numerical example shows that the combination of the genetic algorithm and the nonlinear programming gives faster convergence to the global optimal.

• Measure and Conquer Approach for the Maximum Vertex Weighted Clique Problem

  Huang Fei , Ning Aibing, Liu Zhimin, He Yongmei , Wang Yongfei , Zhang Huizhen

  2017, 37(2): 97-104. doi:

  Abstract ( 2205 )   PDF (284KB) ( 724 )   　　

  Branching and order-reducing are widely used for solving NP-Hard Problems.The main idea of the approach is to solve the problem by decomposing it into two or more sub-problems,and the sub-problems can be recursively solved.But we cannot get a better result by using the normal complexity analyticalmethod since it is not so accurate.The measure and conquer approach is a new technique for algorithm design and complexity analysis.This paper designs an algorithm to solve the weighted maximum clique problem and uses traditional analysis technology to analyze the worst-case running time of the algorithm and gets O(1.4656ⁿp(n))running time,where p(n)is the polynomial function of node number nin the problem.We employ the measure and conquer approach to improve the time complexity of the algorithm from O(1.4656ⁿp(n)) to O (1.3765ⁿp(n))without modifying the algorithm. Our results show that the measure and conquer approach can give more precise time complexity.

• Research on Credit Risk Prevention of Commercial Bank in China Based on Multiple Linear Regression

  Wang Yueheng, Wang Zhong, Xiao Shihao

  2017, 37(2): 105-111. doi:

  Abstract ( 2265 )   PDF (256KB) ( 908 )   　　

  In this paper,the authors analyze the influencing factors and the influence degree of non-performing loans of commercial banks in China by multiple linear regression.The empirical analysis shows that the amount of non-performing loans is affected by the gross domestic product,the ranking of enterprise operating environment,the operation of real estate development units.Among them,the gross domestic product and the ranking of enterprise operating environment are not conducive to the reduction of the credit risk of the commercial banks in China,and the better operation of real estate development and management units,the more conducive to the quality of bank credit assets.

• Quantitative Trading Strategies of Shanghai and Shenzhen 300Index Futures Based on SVM

  Zhang Jian, Wang Bo

  2017, 37(2): 112-121. doi:

  Abstract ( 2168 )   PDF (1789KB) ( 1850 )   　　

  Based on the theory of support vector machine,aquantitative trading model of Shanghai and Shenzhen 300 stock index futures is established.Differing from the regression forecasting method,the model firstly makes use of the advantage of support vector machine in classification in nonlinear systems to transform a complex time series regression prediction problem into a two classification problem by converting the price evolution trend into a transaction signal,and then takes the price information and technical indicators as the input vector,introduces the stop-loss mechanism and obtains the quantitative trading strategy upon the dynamic forecasting model.Empirical results show that the price information transaction strategy has better performance than the technical index trading strategy,and overall,the quantitative trading model has achieved good profit effect.

• Lean Bid Evaluation Method Based on TOPSIS Model

  Li Guoliang, Pang Rongrong, Wang Hongfu, Zhu Rongrong

  2017, 37(2): 122-128. doi:

  Abstract ( 1979 )   PDF (247KB) ( 548 )   　　

  To avoid the drawbacks of the sub-evaluation of electronic evaluation of bidding for construction projects,this paper establishes a lean bid evaluation model based on the theory of lean thinking.Firstly,according to the composition of the project standard of construction project,the index system of bid evaluation model is constructed.Then by applying the method of TOPSIS the bid quotation is evaluated synthetically and the winning bidder is selected.In the bid evaluation,the k-means cluster analysis is used to analyze the tender offer and the weighted average is obtained,and the result is compared with the tender control price to show the competition degree of each unit tender offer. Finally,an example is given to show the practicability and the effectiveness of the lean evaluation model.