Table of Content

15 February 2021, Volume 38 Issue 1 Previous Issue    Next Issue

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Equilibrium Strategies of Fluid Model with Threshold Regulation and Variable Service Rate WANG Shuo, XU Xiu-li 2021, 38 (1):  1-10.  doi: 10.3969/j.issn.1005-3085.2021.01.001 Abstract ( 307 )   PDF (225KB) ( 276 )   Save In a fluid queueing model, maintaining buffers and avoiding system congestion are the focus of attention. For the purpose, this paper combines a threshold regulation with a variable service rate, and studies such a fluid model with the threshold regulation and the variable service rate in a fully observable case. Firstly, the equilibrium balking strategies of fluid are discussed. Secondly, the social benefit per unit time of the model, and the influence of fluid level and threshold on social benefits per unit time are analyzed by numerical examples. Finally, the total revenue of admission fee per unit time is obtained, and the change of the total revenue of admission fee per unit time with the threshold is discussed. The results of this paper will provide theoretical basis for the application of fluid queueing model. Related Articles | Metrics

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Pricing of the Corporate Debt and Optimal Default Boundary in Jump-diffusion Model with $-1$ Jump Size LI Hui-min, LIN Jian-wei 2021, 38 (1):  11-22.  doi: 10.3969/j.issn.1005-3085.2021.01.002 Abstract ( 159 )   PDF (317KB) ( 218 )   Save The default capital reorganization scheme of debt-equity swap is an important solution when the value of the company's assets fluctuated sharply. Under a real market, the paper considers the pricing problems of the corporate debt with the finite maturity in jump-diffusion model with $-1$ jump size. The pricing continuous mathematical model of the corporate equity and debt are constructed by applying a structural method and synthesized the stochastic analysis theory. The existence and uniqueness of an optimal default boundary and the monotonicity of the corporate equity value are proved by a partial differential equation penalty method. At last, the numerical simulation shows that,with the increase of jump intensity, the optimal default boundary of the company decreases, while the stock value increases and the bond value decreases. The attraction of corporate bonds to market investors will be reduced when the company's assets are likely to drop to zero in a flash, equity-holders should reduce the probability of default to improve their credit rating, so as to improve the value of the stock. Related Articles | Metrics

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Change Point Inferences of Risk Premium under the Exponential Premium Principle ZHANG Yi, WEN Li-min, LI Zhi-long 2021, 38 (1):  23-37.  doi: 10.3969/j.issn.1005-3085.2021.01.003 Abstract ( 223 )   PDF (224KB) ( 245 )   Save Premium pricing refers to the process by which an actuary determines a reasonable premium based on the distribution characteristics of the risk. In order to improve the competitiveness of insurance companies, the premiums must be scientific and reasonable and matches the policy risks. However, due to the complexity of risk factors, structural changes in policy risk often lead to changes in premiums, and the detection of premiums is one of the important issues for insurance companies. In this paper, the change point detection model of the exponential premium principle is established. Based on the statistical inference methods in change point theory, the statistic of detecting the change point of the risk premium is proposed, and the estimation of the change point position of the premium is given. Furthermore, the large sample properties and the convergence speed of the estimator are proved. Finally, the numerical simulation method is used to verify the convergence of the statistics, and the accuracy difference of the premium change detection caused by different positions is compared. The method presented in this paper can provide reference value and basis for the insurance company's premium pricing and change detection. Related Articles | Metrics

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An Improved GOM(1,1) Model and Its Application ZHANG Kai, WANG Cheng-yong, HE Li-juan 2021, 38 (1):  38-48.  doi: 10.3969/j.issn.1005-3085.2021.01.004 Abstract ( 203 )   PDF (203KB) ( 266 )   Save In this paper, the modeling and prediction problem of non-negative decreasing sequence are considered. Considering that a grey action will develop and change with the change of the time and space, the grey action is approximately regarded as a linear function of time to construct a GOM(1,1) model with grey action optimization. The optimal background value of GOM(1,1) model is derived by integration based on the non-homogeneous exponential characteristics of the data series of the grey prediction model. Based on the principle of minimum square sum of mean relative error between an original sequence and a simulated sequence, the optimal time response function expression was determined, and the improved algorithm of complete GOM(1,1) model was finally formed. Finally, the effectiveness and practicability of the improved model are verified by an application example. Related Articles | Metrics

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Model and Algorithm of the Bi-level Multiple Followers Linear Programming with Trapezoidal Fuzzy Decision Variables ZHOU Xi-hua, JIA Hong-xin, HUANG Xiao-hong, DENG Sheng-yue, XIE Liang 2021, 38 (1):  49-62.  doi: 10.3969/j.issn.1005-3085.2021.01.005 Abstract ( 157 )   PDF (195KB) ( 288 )   Save The bi-level multiple followers linear programming with trapezoidal fuzzy decision variables model is firstly established in this paper, which is widely applied to multi-level management systems with hierarchical features. By using the fuzzy structured element theory, the ordering of trapezoidal fuzzy numbers is transformed into the ordering of monotone bounded functions through the fuzzy numbers structured element weighted order, and the model's optimal solution is proved to be equivalent to the optimal solution of the bi-level multiple followers linear programming model, and the effective algorithm is designed. Finally, two illustrative numerical examples are provided to demonstrate the feasibility of the proposed method. Related Articles | Metrics

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The Moderate Deviation and Large Deviation for the Smooth Estimate on the m-dependent Sequences XIE Chao, CHEN Xia, YAN Li 2021, 38 (1):  63-72.  doi: 10.3969/j.issn.1005-3085.2021.01.006 Abstract ( 152 )   PDF (177KB) ( 259 )   Save The quantile is an important concept in statistics. It has been widely used in many fields such as reliability statistical analysis, economics, finance, bioinformatics and medicine. The study of the dependent random sequences has received a lot of attention since it weakens the limitation of independence. Therefore, based on the m-dependent sequences, this paper studies the large sample properties of the sample quantile kernel estimation. Firstly, using the limit theorem of m-dependent sequences, the Cramer function is calculated, and the moderate deviation principle of sample quantile kernel estimation is proved. Secondly, by verifying the Cramer condition, large deviation results of the sample quantile kernel estimation are obtained. The proof methods and results of the independent and identically distributed samples are simplified and generalized. Also the results provide an important basis for discussing the moderate deviation and large deviation of other types of dependent sequences. Related Articles | Metrics

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Numerical Simulation of Free Surface for Desingularized Rankine Source Distribution Panel Method HAN Yong-hao, LUO Zhi-qiang 2021, 38 (1):  73-84.  doi: 10.3969/j.issn.1005-3085.2021.01.007 Abstract ( 155 )   PDF (550KB) ( 271 )   Save The near-water surface wave-body interaction is a classical problem in hydrodynamics numerical simulation, and its theory is widely used in ocean engineering and other fields. In this paper is under the circumstance that there are few studies on the variation of underwater oscillatory body and free surface wave in the existing literature. A mathematical model of potential flow underwater cylindrical vibration based on de-singularization Rankine source panel method is established, and the numerical solution of free surface wave elevation of underwater oscillatory cylinder is numerically simulated by Rankine source method. The numerical results of this paper are compared with those of predecessors, and the correctness and validity of this algorithm are verified. Finally, the free surface wave heights under the action of free surface waves and oscillatory cylinders and the surface pressure of oscillatory cylinders under different parameters are numerically simulated. The numerical results show that the free surface wave elevation and the surface pressure of oscillatory cylinders vary with the frequency, amplitude and immersion depth of the oscillatory cylinders. Related Articles | Metrics

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Qualitative Analysis of a Diffusive Predator-prey Model with Allee Effect LI Hai-xia 2021, 38 (1):  85-96.  doi: 10.3969/j.issn.1005-3085.2021.01.008 Abstract ( 186 )   PDF (205KB) ( 256 )   Save The existence, uniqueness and multiplicity of positive solutions to a diffusive predator-prey model with B-D functional response and Allee effect are discussed. By the fixed point index theory, the sufficient conditions for the existence of positive solutions are obtained. Secondly, the conditions for the uniqueness of positive solutions are given by the variational characterization of the lowest eigenvalue. Finally, based on the analysis of positive solutions to two limiting systems, the exact multiplicity and stability of positive solutions are determined by means of the combination of the fixed point index theory, bifurcation theory and perturbation theory of eigenvalues. When the Allee effect constants meet appropriate relationship and the growth rate of the predator is large, the results show that the system has only a unique positive solution when the parameters satisfy certain conditions, and has exactly two positive solutions when the growth rate of the prey lies in a certain range. Related Articles | Metrics

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Large Time Stepping Method for the Modified Cahn-Hilliard Equation HU Huan-huan, LI Yang, JIA Hong-en 2021, 38 (1):  97-109.  doi: 10.3969/j.issn.1005-3085.2021.01.009 Abstract ( 259 )   PDF (5312KB) ( 239 )   Save Over the past decades, the Cahn-Hilliard equation has attracted the attention of many scholars. This equation was originally used to describe the phase separation of two homogeneous mixtures that occurs when the temperature drops and the two mixtures automatically separate and occupy different regions. Along with the theory thorough research, it also has the widespread application in other aspects. The modified Cahn-Hilliard equation enriches the Cahn-Hilliard equation with more properties, and it is a fourth-order nonlinear parabolic equation. Coupled with the small parameter problem of the equation, it is difficult to obtain the exact solution of the equation. Therefore, numerical method can only be used to solve the numerical solution in a small time step. If the solution is carried out in a large time step, the numerical solution will be divergent. A large time step method is proposed in this paper. The proposed scheme is discretized by the finite element method in space and the semi-implicit scheme in time. Stability of the first-order semi-discrete scheme and error estimation of the full discrete scheme are proved. Finally, numerical examples are used to verify the accuracy and validity of the theoretical analysis. Related Articles | Metrics

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A Production Function Model with Seasonal Variations and Its Application CHENG Mao-lin, SHI Guo-jun 2021, 38 (1):  110-120.  doi: 10.3969/j.issn.1005-3085.2021.01.010 Abstract ( 143 )   PDF (134KB) ( 249 )   Save Production function is commonly used in economic the growth factor analysis, among which the CES production function model is an important form, which is more in line with the law of economic growth than the commonly used C-D production function. However, in the analysis, there are many variables that change with the season. For the data that changes with the season, it is obviously not suitable to establish the traditional CES production function model even if the modeling, the error is also very large. Therefore, this paper revises the conventional CES production function and puts forward a CES production function model with seasonal changes. In the application of the model, this paper presents a scientific method to calculate the contribution rate of input factors to economic growth, so as to avoid the large calculation error of the traditional method. Finally, the contribution rate of economic growth factors of real estate industry in China is calculated, and the results are in line with the reality of China. Related Articles | Metrics

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$\Phi$-variational Stability for Measure Functional Differential Equations with Infinite Delay MA Xue-min, ZHANG Huai-de, LI Bao-lin 2021, 38 (1):  121-135.  doi: 10.3969/j.issn.1005-3085.2021.01.011 Abstract ( 149 )   PDF (144KB) ( 259 )   Save In the paper, by using the bounded $\Phi$-variation function,the stability of the bounded $\Phi$-variation solution to measure functional differential equations with infinite delay is discussed. With respect to this kind of equations, the $\Phi$-variational stability, the $\Phi$-variational attraction and asymptotically $\Phi$-variational stability are defined. The Lyapunov type theorems for the $\Phi$-variational stability and asymptotically $\Phi$-variational stability of the bounded $\Phi$-variation solutions are established. These results are essential generalization of the current variational stability theorem for measure functional differential equations with infinite delay. Related Articles | Metrics

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Dynamic Problems in a Decagonal Quasicrystal with a Mode II Griffith Crack ZHOU Jian-min, LI Lian-he, WANG Gui-xia 2021, 38 (1):  136-150.  doi: 10.3969/j.issn.1005-3085.2021.01.012 Abstract ( 138 )   PDF (658KB) ( 246 )   Save Based on the initial boundary value problem of wave-telegraph equations, dynamic problems of the decagonal symmetric two-dimensional quasicrystal material of point group 10mm with a mode II Griffith crack are investigated by using the finite difference method. First, the effects of the loading time, loading location, and specimen size on the crack-tip dynamic stress intensity factor are discussed. Second, the effects of the phonon-phason coupling elastic constant, friction coefficient, and effective mass density on the displacement component of the phason field are discussed, and thus for the movement characteristic of the propagation of the phason wave. The results show that the variation characteristics of the curves corresponding to different related parameters are consistent with the actual physical characteristics. At the same time, while there is a fluctuation characteristic in the phason field, the diffusion characteristic still plays a dominating role. Related Articles | Metrics