Table of Content

15 December 2020, Volume 37 Issue 6 Previous Issue   

Select

Optimal Investment Problem for DC Pension Plan with Return of Death and Accident Clauses CHEN Jia-chen, RONG Xi-min, ZHAO Hui 2020, 37 (6):  651-663.  doi: 10.3969/j.issn.1005-3085.2020.06.001 Abstract ( 159 )   PDF (629KB) ( 248 )   Save This paper studies the optimal investment problem for defined-contribution (DC plan) with the death return and accidental return clauses. In the DC pension plan, the policyholder's contribution rate is determined, and the contribution rate and the investment income of the fund determine the amount of pension that the policyholder will receive in the future. The risk of this kind of pension insurance is entirely borne by the policyholder. Therefore, finding an optimal investment strategy is very important for guaranteeing the policyholder's pension. The insured may have accidents and deaths during the payment process. In order to protect their rights, a predetermined insurance premium should be refunded to the policyholder. The death return and accidental return are described by actuarial symbols and the compound Poisson process, respectively. And the Cram\'{e}r-Lundberg model is used to approximate the compound Poisson process. According to the mean-variance criterion we establish the corresponding Hamilton-Jacobi-Bellmen equations by stochastic control methods and obtain the time-consistent optimal investment strategy influenced by the death and accident of the policyholder. Finally, the effects of model parameters on the efficient frontier and value function are illustrated by numerical. Related Articles | Metrics

Select

Mathematical Modeling of Underground Logistics System WANG Yu-xue, WANG Zi-qiang 2020, 37 (6):  664-672.  doi: 10.3969/j.issn.1005-3085.2020.06.002 Abstract ( 168 )   PDF (297KB) ( 253 )   Save This paper studies the mathematical modeling of underground logistics system based on the theory of optimization. First, we introduce reasonable hypotheses. On this basis, we determine the number and location of the first and second level nodes by the set covering model. Based on the Baumol-Wolfe model, minimizing the total cost as the objective function determines the pipeline construction among the nodes at all levels, the Matlab programming genetic algorithm is used to solve the model, and to get the optimal path. Considering the situation of increasing actual traffic demand, we cluster nodes by traffic volume, confirm the construction route for each construction period, and establish a dynamic sequence evolution diagram. Finally, we summarize and analyze the process and results of the solution. Related Articles | Metrics

Select

Multi-stage Mean-VaR Portfolio Selection Model with Transaction Costs WANG Xiao-qin, GAO Yue-lin 2020, 37 (6):  673-684.  doi: 10.3969/j.issn.1005-3085.2020.06.003 Abstract ( 227 )   PDF (372KB) ( 351 )   Save Taking into account the limitations of risk measures such as variance, lower semi-variance and absolute deviation, and the fact that single-stage investment decision does not accord with investors' actual investment behavior, Value-at-Risk (VaR) is applied in this paper as a measure of risk for multi-stage portfolio optimization. Because short selling is not allowed in Chinese stock market, we consider both transaction costs and investment proportions in constraints and establish a multi-stage mean-VaR portfolio optimization model. Considering that PSO has the advantages of fast convergence, simple structure and less parameters to be regulated, the proposed multi-stage portfolio optimization model is solved by using PSO with penalty function processing mechanism. The optimal investment strategy at each stage under different paths is obtained. It can be seen from the results that the investor's investment behavior is consistent under different investment paths, buying the stocks they are optimistic about in the first stage. After the fluctuation of the stock market in the first stage, the investor continues to buy the stocks which are optimistic in the second stage. Meanwhile, the investor does not buy or sell stocks that are not good. This kind of investment behavior accords with the actual investment behavior of investors. Thus the proposed model is reasonable. Related Articles | Metrics

Select

Optimal Control of $M/M/1$ Production Inventory System with Positive Service Time and Perishable Items WANG Sai, YUE De-quan, ZHANG Yuan-yuan, TIAN Rui-ling 2020, 37 (6):  685-698.  doi: 10.3969/j.issn.1005-3085.2020.06.004 Abstract ( 143 )   PDF (221KB) ( 263 )   Save The $M/M/1$ production-service-inventory model with perishable products is studied. The life time of the perishable product, the production time and the service time are all assumed to be exponentially distributed. Firstly, the steady-state equilibrium condition of the model is obtained by using the quasi-birth-and-death process theory. Secondly, the matrix geometric solution of the steady-state probability vector is obtained, and the calculation formulas of the performance index and cost function are obtained. Finally, the genetic algorithm is used to analyze the sensitivity of the model's optimal production inventory strategy and the effect of system parameters on performance indexes. The results of this paper can provide some theoretical basis for inventory managers of production companies. Related Articles | Metrics

Select

The 0-1 Ant Colony Conditional Coloring Resolving Algorithm for Solving the Metric Dimension Problem of Graphs WU Jian, ZHAO Hai-xia 2020, 37 (6):  699-718.  doi: 10.3969/j.issn.1005-3085.2020.06.005 Abstract ( 158 )   PDF (297KB) ( 196 )   Save The metric dimension problem (MDP) of graphs is a kind of combinatorial optimization problem which has important applications in the fields such as machine navigation, sonar system layout, chemistry, and data classification. To solve this problem, we establish a non-linear model by introducing a resolving table storage structure for the considered graphs; simultaneously, an improved ant colony algorithm for solving the proposed model is established, by improving the parameters design of existing ant colony algorithms and leveraging the strategy of global search and local search. Numerical comparison analysis verifies the efficiency of the new algorithm: the combination of global search and local search improves the solution quality of the proposed algorithm to a large extent; it is a great challenge to improve the solution quality of the algorithm on regular graphs; compared with the results of genetic algorithm on MDP, the algorithm proposed in this paper not only improves the solution quality, but also provides the minimal resolving set for graphs in the worst case. Furthermore, we examine the influences of some parameters on the solution quality of the algorithm, and propose a further research topic. Related Articles | Metrics

Select

Positivity-preserving Scheme of 1D Convection-diffusion Equation on Nonuniform Meshes LAN Bin, WANG Tao 2020, 37 (6):  719-729.  doi: 10.3969/j.issn.1005-3085.2020.06.006 Abstract ( 131 )   PDF (224KB) ( 371 )   Save The convection diffusion equation exists widely in many fields. In order to solve some practical problems, the discretization scheme should not only satisfy some basic properties, such as convergence, stability and the existence and uniqueness of solutions, but also keep the positivity of the discretization scheme. A lot of researches has been done to solve the convection diffusion equation by using the finite volume scheme, but little work has been done in the aspect of keeping the positivity. In this paper, a nolinear positivity-preserving finite volume scheme for the one-dimensional convection diffusion equation on arbitrary nonuniform grids is constructed. The scheme is unformed in a matrix form. Then, it is proved that the scheme satisfies the requirement of positivity-preserving by using the properties of the coefficient matrix. The scheme only contains the unknown quantity of the center of the interval element and satisfies the local conservation of flux at the end of the interval. Finally, the numerical results show that the proposed scheme is effective and owns the second order accuracy. In addition, the scheme is applicable to the solution of problems with discontinuous diffusion coefficients. Related Articles | Metrics

Select

A Delayed Predator-prey-environment Model with Impulsive Harvesting and Pulse Input of Pollutant ZHANG Pei-jun, WANG Zhen, CHEN Heng 2020, 37 (6):  731-741.  doi: 10.3969/j.issn.1005-3085.2020.06.007 Abstract ( 108 )   PDF (272KB) ( 219 )   Save Established in this paper is a time-delay predator-prey-environment model with stage structure of predator, impulsive harvesting of prey and impulsive input of pollutant in polluted environment. By using the stroboscopic mapping and the comparison principle of discrete dynamical systems, sufficient conditions for the global attractiveness of the predator extinction periodic solution and system persistence are obtained. Through numerical simulation, the effects of the prey capture, pulse input of pollutants and pulse action period on the extinction and survival of predators are studied, and the theoretical results are verified. It provides valuable theoretical basis for the development of biological resources, the harvest of population number and the control of environment. Related Articles | Metrics

Select

Finite-time Synchronization of Fractional-order Victor-Carmen Systems with Dead-zone Input CHENG Chun-rui, MAO Bei-xing, WANG Dong-xiao 2020, 37 (6):  742-752.  doi: 10.3969/j.issn.1005-3085.2020.06.008 Abstract ( 150 )   PDF (385KB) ( 410 )   Save The finite-time control method is an effective technique to obtain fast convergence in a control system. It is more advantageous to synchronize chaotic systems within a finite time rather than merely asymptotically. This paper is concerned with the finite-time synchronization problem of fractional-order Victor-Carmen system with dead-zone input. To ensure that Victor-Carmen system states converge to the equilibrium point in a given finite time, an adaptive sliding mode control strategy is proposed. A non-singular fractional-order sliding surface is designed and an adaptive sliding mode control law is introduced to force the trajectory of the synchronization error systems onto the sliding surface, chaos synchronization is thus achieved for master-slave systems. The illustrative examples are presented to illustrate the effectiveness and applicability of the proposed finite-time controller and to validate the theoretical results of the paper. Related Articles | Metrics

Select

Second-order Partitioned Time Stepping Methods for a Parabolic Two Domain Problem YAN Wei, SHAN Li, DONG Chun-sheng 2020, 37 (6):  753-771.  doi: 10.3969/j.issn.1005-3085.2020.06.009 Abstract ( 137 )   PDF (178KB) ( 408 )   Save The atmosphere-ocean interaction can be modeled by a fluid-fluid system which coupled by some interface conditions. It is pretty important to study the robust numerical methods for the two domain coupling problem. In this paper, we study a simplified model of diffusion through two adjacent materials which are coupled across their shared interface. Two second-order partitioned time stepping schemes are proposed. Both schemes only require the solution of two decoupled parabolic problems at each time step. Hence, they are efficient in computation and can be easily implemented by using legacy codes. We also analyze their unconditional stabilities and convergence results, together with the numerical experiments, which verify our theoretical results. Related Articles | Metrics

Select

A New Ger\v{s}gorin-type Eigenvalue Localization Set for Stochastic Matrices ZHU Yan, ZHOU Bao-xing, LI Yao-tang 2020, 37 (6):  771-780.  doi: 10.3969/j.issn.1005-3085.2020.06.010 Abstract ( 118 )   PDF (15584KB) ( 52 )   Save Stochastic matrix and its eigenvalue localization play key roles in many application fields such as computer aided geometric design, mathematical economics and Markov chain. Stochastic matrix eigenvalue problem contains mainly two aspects: providing a region which contains all eigenvalues different from 1 for stochastic matrices in the complex plane; estimating approximately the gap between the dominant eigenvalue 1 and the cluster of all other eigenvalues. In this paper, we localize and estimate the eigenvalues different from 1 of stochastic matrices and obtain the following results: first, we obtain a new and simple region which includes all eigenvalues of a stochastic matrix different from 1 by refining the Ger\v{s}gorin circle. Furthermore, an algorithm is proposed to estimate an upper bound for the spectral gap of the subdominant eigenvalue of a positive stochastic matrix. Numerical examples illustrate that the proposed results are effective. Related Articles | Metrics