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15 February 2020, Volume 37 Issue 1 Previous Issue    Next Issue

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Multi-product Newsvendor Problem with Constraints of Second Order Stochastic Dominance and Order Capability FU Yong-bin, SUN Hai-lin 2020, 37 (1):  1-15.  doi: 10.3969/j.issn.1005-3085.2020.01.001 Abstract ( 448 )   PDF (236KB) ( 358 )   Save Under on uncertain environment, using risk measure to resist the future uncertainties is an important way to avoid risks in newsvendor problem. Second order Stochastic Dominance (SSD) can be used as a robust risk measure. In this paper, we propose a risk aversion multi-product newsvendor model (SSD model) with SSD constraints and capability constraint. Moreover, the sample average approximation (SAA) method is used to approximate the problem, and the convergence analysis of the SAA problem is studied. Finally, in the numerical experiments section, we use the cutting plane method to solve SAA problem, at the same time it is compared with the reference models based on risk neutral (without risk constraints) and risk aversion (with variance as risk constraints). The numerical results show that the SSD model can avoid risks better and get higher return than the reference models under out-of-sample forecast. Related Articles | Metrics

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Pricing of Perpetual Corporate Debt with Bankruptcy Reorganization in a Double Exponential Jump-diffusion Model LIN Jian-wei, LI Hui-min 2020, 37 (1):  16-26.  doi: 10.3969/j.issn.1005-3085.2020.01.002 Abstract ( 297 )   PDF (185KB) ( 647 )   Save In order to better deal with the risk of the asset jump and the strategy of bank-ruptcy reorganization faced by the company, based on a structural method and the optimal stopping technique, this paper considers the pricing problem of the perpetual corporate debt with the bankruptcy reorganization scheme of debt-equity swap in a double jump-diffusion model. Pricing analytical solutions of the perpetual corporate debt and the equity are obtained by a differential equation method. Furthermore, this paper also presents a closed-form solution of the optimal bankruptcy boundary and a nonlinear equation satisfied by the optimal coupon. Finally, the numerical results show that more volatile the company's asset value is, more income equityholders can be gotten from the turbulent market, but less popular the corporate debt will be with investors, lower the value of corporate debt is and lower the optimal leverage ratio is. Related Articles | Metrics

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Dynamical Behavior Analysis of a Generalized Single-species Population Model in a Polluted Environment CAO Ming, WANG Xia, TANG San-yi 2020, 37 (1):  27-42.  doi: 10.3969/j.issn.1005-3085.2020.01.003 Abstract ( 238 )   PDF (463KB) ( 288 )   Save The environmental pollution problem caused by the rapid development of modern industry and agriculture and other production activities has become one of the most important ecological problems. In this paper, a new generalized single-species population model in polluted environment is established to study the influence of environmental toxins and food chain toxins on the existence of the specie. By using the average integral method, sufficient conditions for uniform persistence, non-persistent in the mean, weak persistence in the mean and extinction, and the threshold between weak persistence and extinction of the population are obtained. These results provide reliable scientific basis for the conservation of species and the management of the environment. Related Articles | Metrics

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Two Conservative Compact Finite Difference Schemes for the Long-wave Short-wave Interaction Equation JIANG Jia-ping, WANG Ting-chun 2020, 37 (1):  43-55.  doi: 10.3969/j.issn.1005-3085.2020.01.004 Abstract ( 271 )   PDF (499KB) ( 308 )   Save This paper focuses on numerical simulation of the long-wave short-wave interaction equation. Two fourth-order compact finite difference schemes are proposed and proved to preserve the total mass and energy in the discrete sense. Numerical results show the good stability of the schemes and fourth-order and second-order convergence of the numerical solutions in space and time, respectively. Simulation results also show that the schemes preserve well the total mass and energy. Related Articles | Metrics

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A New Application of the Extended Tanh-function Method and New Solutions of the Riccati Equation and sine-Gordon Equation LIN Fu-biao, ZHANG Qian-hong 2020, 37 (1):  56-66.  doi: 10.3969/j.issn.1005-3085.2020.01.005 Abstract ( 261 )   PDF (360KB) ( 480 )   Save The explicit analytical solutions of nonlinear partial differential equations, in particular, the travelling wave solutions, contain rich information about the equations, and they are very important for describing the development of various phenomena. In the paper, many types of new explicit travelling wave solutions are presented for the KdV equation. First, many new explicit analytical solutions of the Riccati equation are given by using the trial function method and Matlab software. Second, many types of new explicit analytical solutions of the sine-Gordon equation are obtained by using the extended tanh-function method and new solutions of Riccati equation. Finally, as a new application, a great many new travelling wave solutions of the KdV equation are provided by using the sine-cosine function method, new solutions of the sine-Gordon equation and its simplified transformation forms. The obtained results extend and complement some relevant existing works. In particular, these methods and obtained new results can be applied to find explicit new travelling wave solutions of many nonlinear partial differential equations. Related Articles | Metrics

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Improved Alternating-direction Implicit Iterative Scheme for Poisson Equation GE Zhi-hao, LIU Fu-hao 2020, 37 (1):  67-74.  doi: 10.3969/j.issn.1005-3085.2020.01.006 Abstract ( 362 )   PDF (805KB) ( 545 )   Save In this paper, we improve the iterative scheme of alternating-direction implicit iterative method for Poisson equation, which reduces the difficulty and complexity of the calculating process by solving the lower dimension matrix equations in each iterative step. Taking the Gauss elimination method as an example, we estimate the computation of the improved alternating-direction implicit iterative scheme and find that the computation cost is much less than one of the classical alternating-direction implicit iterative scheme. Also, we prove the equivalence between the improved iterative scheme and the classical iterative scheme. Finally, we give the numerical tests to verify the advantage of the improved iterative scheme. Related Articles | Metrics

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New Criteria for Nonsingular $H$-matrices LIU Chang-tai, XU Jing, XU Hui-jun 2020, 37 (1):  75-88.  doi: 10.3969/j.issn.1005-3085.2020.01.007 Abstract ( 228 )   PDF (157KB) ( 254 )   Save To determine a given matrix is a  nonsingular $H$-matrix or not plays an important role in mathematical economics, control theory, and so on. To get more nonsingular $H$-matrices easily, several practical sufficient conditions for nonsingular $H$-matrices  are  obtained by constructing exquisite positive diagonal matrices and applying some technical of inequalities. The corresponding results are improved and extended. Advantages of these results are illustrated by a numerical example. Related Articles | Metrics

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Gerber-Shiu Analysis for a Discrete Risk Model with Delayed Claims and Random Incomes HUANG Ya, LIU Juan, ZHOU Jie-ming, DENG Ying-chun 2020, 37 (1):  89-106.  doi: 10.3969/j.issn.1005-3085.2020.01.008 Abstract ( 175 )   PDF (154KB) ( 286 )   Save Ruin theory is the mainly contents of insurance mathematics, as it can supply a very useful early-warning measure for the risk of the insurance company. In this paper, we study a risk model with potentially delayed claims and random premium incomes within the framework of the compound binomial model. Using the technique of generating functions, we derive a recursive formula for the Gerber-Shiu expected discounted penalty function. Specifically, an explicit formula is obtained for the discount-free case. As applications, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin. Related Articles | Metrics

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Emphatic Convergence for Kurzweil Equations MA Xue-min, ZHANG Ling, LI Bao-lin 2020, 37 (1):  107-120.  doi: 10.3969/j.issn.1005-3085.2020.01.009 Abstract ( 209 )   PDF (129KB) ( 410 )   Save In this paper, by using the theories of Kurzweil integral and bounded $\Phi$-variation function. Emphatic convergence for Kurzweil equations and its application for a sequence of ordinary differential equations are discussed. The theorem of emphatic convergence for bounded $\Phi$-variation solutions of Kurzweil equations is obtained. The result is continuation of continuous dependence of bounded $\Phi$-variation solutions on parameters for Kurzweil equations and essential generalization of the emphatic convergence for bounded variation solutions of Kurzweil equations. Related Articles | Metrics

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The Bicyclic Graph with the Minimum Distance Laplacian Spectral Radius FAN Dan-dan, NIU Ai-hong, WANG Guo-ping 2020, 37 (1):  121-130.  doi: 10.3969/j.issn.1005-3085.2020.01.010 Abstract ( 213 )   PDF (160KB) ( 310 )   Save The largest eigenvalue of the distance Laplacian matrix of a connected graph G is called the distance Laplacian spectral radius of the graph $G$. In this paper we obtain a sharp lower bound of distance Laplacian spectral radius, and then using the bound we determine the unique graph which has the minimum distance Laplacian spectral radius among all unicyclic graphs. Finally, by using the bound again as well as the characteristics polynomial of a distance Laplacian matrix, we characterize the unique graph with the minimum distance Laplacian spectral radius among all bicyclic graphs. Related Articles | Metrics