Table of Content

15 August 2015, Volume 32 Issue 4 Previous Issue    Next Issue

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Construction of Equivalent Martingale Measure in the Regime-switching Model ZHAO Pan, XIAO Qing-xian 2015, 32 (4):  475-484.  doi: 10.3969/j.issn.1005-3085.2015.04.001 Abstract ( 18 )   PDF (182KB) ( 5 )   Save Price models with regime switching can describe the impact of macroeconomics. However, when constructing an equivalent martingale measure to price financial derivatives, the equivalent martingale measure obtained by the traditional Esscher transform considers only micro-marketing risks but not macroeconomic risks represented by the regime switching. In addition, the classical geometric Brownian motion can not characterize higher peak and fat tail phenomena of asset returns. In this paper, firstly, by using a Markov process and a non-extensive maximum entropy distribution, a new price model which can describe both the phenomena of higher peak, fat tail and regime-switching is constructed. Then, by utilizing the martingale theory and the product of the price process of micro market and the Markov process of macroeconomics, a new method for constructing equivalent martingale measure is provided. The equivalent martingale measure obtained by this approach includes two kinds of risks: micro-marketing risks and macroeconomic risks. Finally, under the resulted equivalent martingale measure, the necessary and sufficient conditions are given with which the discounted asset price process can become a martingale. The results provide a theoretical basis for further studying derivative pricing and risk control. Related Articles | Metrics

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P-spline Estimation for Short-term Interest Rate Model JIANG Liang, LIN Hong-xi 2015, 32 (4):  485-496.  doi: 10.3969/j.issn.1005-3085.2015.04.002 Abstract ( 21 )   PDF (747KB) ( 3 )   Save Since the mean reverting is a function in the Hull-White model, this paper develops the estimator and provides the estimation of the mean revering function, which will be estimated by using P-spline estimator and other constant parameters. In addition, we also present an alternative approach to select the regularization parameter. Furthermore, we prove the consistency of the two-stage method and its asymptotic normality of parameters. Finally, based on the zero coupon bond price data, empirical evidences show that there is a slightly less difference between the goodness-of-fit and the constant parameter estimates arising from the bond price less sensitive to short-term rate. Related Articles | Metrics

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New Hesitant Fuzzy Linguistic TOPSIS with Partly Known Attribute Weight Information LIU Yong, WANG Cheng-jun, YANG Wei 2015, 32 (4):  497-506.  doi: 10.3969/j.issn.1005-3085.2015.04.003 Abstract ( 20 )   PDF (175KB) ( 4 )   Save Uncertain information modeled by linguistic arguments and fuzzy memberships, a new multiple attribute decision making method, has been proposed with partly known attribute weight information. First we use linguistic arguments and fuzzy memberships to model uncertain information, then a linear programming by using the maximum deviation method is set up to determine the attribute weights, and next the TOPSIS is used to rank the alternatives. We apply the proposed methods to evaluating paintings in Xi'an subway to illustrate its efficiency and practical advantages. Numerical example substantiates the effectiveness of the proposed method. Related Articles | Metrics

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MAP$_{1}$, MAP$_{2}/M/c/N$ Retrial Queueing Model with Non-preemptive Priority ZHOU Zong-hao, ZHOU Zhen-chuan, ZHU Yi-jun, SHI Zhi-yan 2015, 32 (4):  507-516.  doi: 10.3969/j.issn.1005-3085.2015.04.004 Abstract ( 23 )   PDF (363KB) ( 5 )   Save In order to study the influence of the priority queueing policy and different types of input flows on the retrial queueing model indexes in communication networks, this paper constructs a retrial queueing model with non-preemptive priority in which arrival processes of ordinary and priority customers are different arrival rate Markov processes. The main queueing indexes and system steady state condition of the system are derived by the quasi birth-and-death process and matrix analysis. By means of numerical simulation, we found that Markov arrival input flows are more likely to lead to congestion of the system than Poison input flows do, and the priory customer arrival rate is more likely to lead to congestion of the system than the ordinary customers do. Related Articles | Metrics

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The Study of Black-Litterman Model Based on Multi-index Information Ranking Method FANG Zheng, CHENG Xi-jun, GE Ying 2015, 32 (4):  517-523.  doi: 10.3969/j.issn.1005-3085.2015.04.005 Abstract ( 19 )   PDF (214KB) ( 4 )   Save In order to solve the problem that the viewpoints of investors are difficult to be quantified in Black-Litterman model, we propose a new model incorporated in multi-indicators sequencing based on the TOPSIS method. Firstly, quantitative viewpoint matrix is determined by using the multi-indicators sequence of assets, which is designed based on TOPSIS. Secondly, we apply the means of latest stochastic optimization to obtain the weights of portfolio. Finally, empirical research is studied by selecting several stocks in Shanghai Stock Exchange Market used for asset allocation. Empirical results reveal that as compared with other traditional portfolio methods, our new means can effectively include additional information except price, which leads to improvement of the robustness and application of the proposed model. Related Articles | Metrics

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The Bahadur Representation for the Estimator of Sample Quantiles under Positive Associated Samples LI Yong-ming, ZHANG Wen-ting, LI Nai-yi, YAO Jing 2015, 32 (4):  524-532.  doi: 10.3969/j.issn.1005-3085.2015.04.006 Abstract ( 20 )   PDF (155KB) ( 4 )   Save The positively associated sequence is a general class of random variables, and has been widely utilized in multivariate statistical analysis and system reliability. The purpose of this paper is to estimate sample quantiles based on a stationary and positively associated sequ-ence. By applying the property of a positively associated sequence, we establish a covariance inequality for the positively associated variables. And then, by using the exponential inequality of a positively associated sequence, we obtain an inequality for the empirical distribution function. Furthermore, under certain conditions, by virtue of the obtained inequality, we discuss the consistency of the sample quantile estimator for positively associated sequence, and derive the Bahadur representation together with its convergence rate. Related Articles | Metrics

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Optimal Convergence Order Analysis of a Block-by-block Algorithm for Fractional Differential Equations WANG Zi-qiang, CAO Jun-ying 2015, 32 (4):  533-545.  doi: 10.3969/j.issn.1005-3085.2015.04.007 Abstract ( 21 )   PDF (163KB) ( 3 )   Save The classic block-by-block method is a highly efficient numerical method to solve the integral equation. Using the classic block-by-block method, researchers have successfully constructed higher order numerical methods for nonlinear fractional ordinary differential equ-ation, and made preliminary analysis on the convergence of this numerical method. But the results of numerical experiments show that the theoretical analysis does not achieve the optimal error estimate order. Based on the Taylor formula and integral mean value theorem, this article makes a thorough analyses on the block-by-block method of nonlinear fractional ordinary differential equations and obtains the optimal error estimate order. Finally numerical experiments are carried out to support the theoretical claims. Related Articles | Metrics

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A Spectral Element Method for Human Carotid Atherosclerotic Plaques SONG Fang-ying, LIU Xiao-ling, XU Chuan-ju 2015, 32 (4):  546-556.  doi: 10.3969/j.issn.1005-3085.2015.04.008 Abstract ( 18 )   PDF (776KB) ( 3 )   Save In this paper, we propose a numerical method for the elastic equation governing the blood driven motion of human carotid atherosclerotic plaques. The proposed schema combines a spectral element method for the spatial discretization and a Newmark-like method for the time discretization. We obtain the optimal error estimate for the numerical solution to the full-discrete problem, showing that the convergence is exponential in space and of second order in time. It is also proven that the overall schema is unconditionally stable in certain cases. Finally, we present some numerical examples to verify the error estimates, and carry out a simulation in an application domain extracted from practical experiments. Related Articles | Metrics

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The Bifurcation of a Class of Leslie-Gower Predator-prey Models LI Rui, LI Yan-ling 2015, 32 (4):  557-567.  doi: 10.3969/j.issn.1005-3085.2015.04.009 Abstract ( 19 )   PDF (164KB) ( 4 )   Save A Leslie-Gower model with diffusion under homogeneous Neumann boundary condition is investigated in this paper. Firstly, the local stability of the constant steady-state is obtained by using the theory of spectral analysis and stability; secondly, by using the maximum principle, Harnack inequalities and energy method, the estimate of the upper and positive lower bound and nonexistence of nonconstant positive steady-state solution are obtained; by further applying simple eigenvalue bifurcation theory, the local bifurcations from the two constant solu-tions and the existence of nonconstant steady-state are given; finally, the constant solution where Hopf bifurcation occurs is obtained by using Hopf bifurcation theory. Related Articles | Metrics

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Existence of Periodic Solutions of Fourth-order Nonlinear Difference Equations WU Yun-zong, SHI Hai-ping, GUO Cheng-jun 2015, 32 (4):  568-576.  doi: 10.3969/j.issn.1005-3085.2015.04.010 Abstract ( 21 )   PDF (158KB) ( 4 )   Save In this paper, the existence of periodic solutions to a fourth-order nonlinear difference equation is studied. First, a variational functional corresponding to the difference equations as aforementioned is established. Next, the existence of periodic solutions can be simplified as the existence of critical point of the functional. By using critical point theory and some decomposition techniques of space, the sufficient conditions for the existence of a periodic solution are obtained. The practical effectiveness of our main theorem in view of an example is illustrated. Main results of this paper are helpful to enrich the theory of periodic solutions to fourth-order difference equations. Related Articles | Metrics

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Numerical Approximation to a Shallow Wave Model with a Nonlocal Viscous ZHANG Jun, LI Wu-lan 2015, 32 (4):  577-589.  doi: 10.3969/j.issn.1005-3085.2015.04.011 Abstract ( 24 )   PDF (459KB) ( 3 )   Save We focus on the numerical investigation of a water wave model with a nonlocal viscous dispersive term. We construct and analyze a schema to numerically solving the nonlocal water wave model. The key for the success consists in a particular combination of the treatments for the nonlocal dispersive term and nonlinear convection term. The proposed methods employ a known $(2-\alpha)$-order schema for the $\alpha$-order fractional derivative and a mixed linearization of the nonlinear term. A rigorous analysis shows that the proposed schema is unconditionally stable, and the linearized  Crank-Nicolson plus $(2-\alpha)$--order schemes is ${O}( \Delta t^{\frac{3}{2}} +N^{1-m})$. A series of numerical examples is presented to confirm the theoretical prediction. Finally the proposed methods are used to investigate the asymptotical decay rate of the solutions of the nonlocal viscous wave equation, as well as the impact of different terms on this decay rate. Related Articles | Metrics

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Comparisons on Order Statistics from Heterogeneous Inverse Weibull Distributions QIU Guo-xin, JIANG Hai-bo 2015, 32 (4):  590-598.  doi: 10.3969/j.issn.1005-3085.2015.04.012 Abstract ( 24 )   PDF (122KB) ( 3 )   Save In this paper, we consider two different systems consisting of independent components with inverse Weibull distributions whose characteristic life parameters are heterogeneous, but the shape parameters are common. It is shown that the survival function (hazard rate) of a series system is decreasing in the characteristic life parameter vector with respect to $p$-larger (majorization) ordering. It is also shown that the reversed hazard rate of a parallel system is decreasing (increasing) in characteristic life parameter vector with respect to majorization ordering if the common shape parameters are less (greater) than $1$. As a consequence, the simple upper bound on the survival function of the series (parallel) systems is built in terms of geometric (arithmetic) mean of the characteristic life parameters. Related Articles | Metrics

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Solvability and Positivity of Fractional Descriptor Systems DING Xiao-li 2015, 32 (4):  599-607.  doi: 10.3969/j.issn.1005-3085.2015.04.013 Abstract ( 19 )   PDF (103KB) ( 3 )   Save Fractional descriptor systems belong to an important class of fractional differential systems. The systems have a wide range of applications in physical and engineering problems such as integrated circuits with superconductor materials. In this paper, a new class of fractional descriptor systems is considered and solvability of the fractional descriptor systems is discussed. Furthermore, explicit solutions of the fractional descriptor systems are given and sufficient conditions for the positivity of the fractional descriptor systems are established. An example is presented to illustrate the feasibility and applications of the obtained results. Our results can be extended to the case of fractional descriptor systems with different fractional orders. Related Articles | Metrics

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An Average Criterion for Global Exponential Stability of Periodic CNNs with Delay and Impulses SONG Xue-li, ZHAO Pan, WANG Xiao-wei 2015, 32 (4):  608-622.  doi: 10.3969/j.issn.1005-3085.2015.04.014 Abstract ( 20 )   PDF (156KB) ( 3 )   Save This paper investigates the global exponential stability of non-autonomous impulsive and delayed cellular neural networks with periodic coefficients. Particularly, by means of the nonlinear measure method and periodic Halanay differential inequality, we obtain an integral average criterion for global exponential stability of this class of neural networks. Our method does not require assumptions on boundedness and monotonicity of activation functions, which demonstrates that our derived criterion is less restrictive than some existing ones and can be applied to more general practical problems. Moreover, our stability criterion is the generalization and improvement of some existing ones. Finally, an example illustrates the effectiveness of our method and the correctness of our results. Related Articles | Metrics

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Discontinuity Identification for Heat Conduction Problem Based on the Adjoint Method YAN Wen-jing, DUAN Xian-bao, GUAN Guo-xing 2015, 32 (4):  623-632.  doi: 10.3969/j.issn.1005-3085.2015.04.015 Abstract ( 18 )   PDF (951KB) ( 4 )   Save In this paper, we consider the shape inverse problem of discontinuity identification for the heat conduction. Based on the continuous adjoint method, we derive the structure of the derivative for the cost functional by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape inverse problem. Finally, numerical results demonstrate the feasibility and effectiveness of the proposed algorithm. Related Articles | Metrics