Table of Content

15 April 2016, Volume 33 Issue 2 Previous Issue    Next Issue

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The Stochastic Actuarial Models and Simulation about Retirement Annuity under Flexible Retirement System SUN Rong 2016, 33 (2):  111-120.  doi: 10.3969/j.issn.1005-3085.2016.02.001 Abstract ( 16 )   PDF (209KB) ( 3 )   Save The flexible retirement system is one of the options of society endowment insurance system to deal with the aging. Therefore, the pension annuity under the system has important impact on theory and practice. This paper investigates the actuarial function of retirement annuity under the flexible retirement system. Under the hypothesis that the distribution of the retirement age is binomial distribution, the interest rate is decided by the discontinuous stochastic differential equations with jumps, and the death intensity is decided by Feller process with a jump. The formulas of the retirement annuity are proposed, including the life annuities, insurance, net premiums and insurance actuarial present value of second moment, and the simulatived estimation for the relevant actuarial functions is derived. These formulas provide the basis of the actuarial analysis of insurance and balance insurance under the flexible retirement system, thus they can be applied for the old-age insurance system and control of risk pension account in China. Related Articles | Metrics

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Gerber-Shiu Discounted Penalty Function for Compound Poisson-Geometric Risk Model with Variable Premium Rate HE Li-juan, WANG Cheng-yong, ZHANG Kai 2016, 33 (2):  121-130.  doi: 10.3969/j.issn.1005-3085.2016.02.002 Abstract ( 20 )   PDF (272KB) ( 4 )   Save In this paper, we consider a new risk model of compound Poisson-Geometric process which assumes that the insurance company receives the premium with a differentiable rate. By applying the differential argument method, a defective renewal equation of Gerber-Shiu discounted penalty function is obtained. Based on the results, the defective renewal equation of the ruin probability, the moments of the surplus immediately prior to ruin and the deficit at ruin have been deduced. By solving the differential equation, the inequality which the ruin probability satisfied have been obtained when the claim variable random belongs to the exponential distribution. Moreover, numerical analysis of the distribution is presented and some examples are given. Finally, we conclude that the impacts of the adjustment policy and the premium policy to the insurance company. Related Articles | Metrics

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Optimal Shape Design of Stokes Problem by Adaptive Mesh Method DUAN Xian-bao, LI Fei-fei, QIN Xin-qiang 2016, 33 (2):  131-137.  doi: 10.3969/j.issn.1005-3085.2016.02.003 Abstract ( 21 )   PDF (341KB) ( 4 )   Save In order to solve optimal shape design problem arising from fluid dynamics, an optimality criteria (OC) coupled adaptive mesh refinement algorithm has been presented in this paper. The objective is to minimize the dissipated power in the fluid, subject to the Stokes problem as the state equations. By this method, higher resolution of the interface can be obtained with a minimum of additional expense. A material distribution information based indicator is adopted during the automatic local adaptive mesh refinement process. Although only considered the Stokes problem in this study, the proposed method can be applied to a wide range of optimal shape or topology design problems in fluid dynamics. Related Articles | Metrics

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Stability Analysis on a Ratio-dependent Predator-prey Model with Time Delay and Stage Structure WANG Ling-shu, ZHANG Ya-nan, FENG Guang-hui 2016, 33 (2):  138-150.  doi: 10.3969/j.issn.1005-3085.2016.02.004 Abstract ( 26 )   PDF (160KB) ( 10 )   Save In this paper, a ratio-dependent predator-prey model with time delay due to the gestation of the predator and stage structure for both the predator and the prey is investigated. By analyzing the characteristic equations and applying Hurwitz criterion, the local stability of a semi-trivial boundary equilibrium and a positive equilibrium are discussed, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By comparison arguments and iteration technique, the global stability of the semi-trivial boundary equilibrium and the positive equilibrium are addressed, respectively. Related Articles | Metrics

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Simulation of Two-dimensional Planar Contraction Flow Based on Brownian Configuration Fields Method LI Lu-cheng, XU Xiao-yang 2016, 33 (2):  151-162.  doi: 10.3969/j.issn.1005-3085.2016.02.005 Abstract ( 20 )   PDF (1150KB) ( 8 )   Save In this paper, Brownian configuration fields (BCF) with the finite volume discretization on non-staggered grids is employed to simulate 2D viscoelastic fluid flows. In order to verify the effectiveness of the numerical method, the plane Couette flow is firstly tested, and the resu-lts are compared with the available literature data. Then, the BCF method is extended to the planar contraction flow. The influence of We on the flow patterns is also analyzed. All numerical results illustrate that the numerical method employed in this paper has the advantages of high efficiency and good stability, and is easy to deal with the convection term. Furthermore, it is observed that the variance reduction can nicely suppress the unphysical oscillation of stress around the contraction corner. Related Articles | Metrics

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A Set of Determinate Conditions for Nonsingular $H$-matrices CUI Jing-jing, LU Quan, XU Zhong, AN Xiao-hong 2016, 33 (2):  163-174.  doi: 10.3969/j.issn.1005-3085.2016.02.006 Abstract ( 28 )   PDF (167KB) ( 4 )   Save Nonsingular $H$-matrices has a wide range of applications in computational mathematics, physical mathematics, biology, matrix theory and control theory, etc. How to specify nonsingular $H$-matrices effectively has always been paid attention. In the paper, by applying $k$-partition of matrices index set, a set of determinate conditions for nonsingular $H$-matrices are given, which improve and generalize some recent related results. The effectiveness of these determinate conditions in this paper is illustrated with numerical examples. Related Articles | Metrics

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Global Stability of an SEIR Epidemic Model with Nonlinear Incidence SONG Xiu-chao, LI Jian-quan, YANG Ya-li 2016, 33 (2):  175-183.  doi: 10.3969/j.issn.1005-3085.2016.02.007 Abstract ( 26 )   PDF (163KB) ( 6 )   Save In this paper, an SEIR epidemic model with nonlinear incidence is investigated. By applying the next generation matrix, the basic reproduction number determining whether the disease dies is found, and the existence of the equilibria of the model is discussed; according to the suitable Lyapunov function and the LaSalle invariance principle, it is proved that the disease free equilibrium is globally asymptotically stable as the basic reproduction number is less than or equal to unity; by means of the Lyapunov direct method, it is testified that the endemic equilibrium is globally asymptotically stable as the basic reproduction number is greater than unity. Finally, the theoretical results obtained here are verified by numerical simulations for the SEIR model with a specific incidence. Related Articles | Metrics

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Anti-plane Analysis of a Circular Hole with Three Unequal Cracks in One-dimensional Hexagonal Piezoelectric Quasicrystals YANG Juan, LI Xing, DING Sheng-hu 2016, 33 (2):  184-198.  doi: 10.3969/j.issn.1005-3085.2016.02.008 Abstract ( 26 )   PDF (168KB) ( 6 )   Save This paper employes variable function method and the technique of conformal mapping to discuss the anti-plane problem of a circular hole with three unequal cracks in a one-dimensional (1D) hexagonal piezoelectric quasicrystal. Based on the piezoelectricity fundamental equations of quasicrystal materials and the symmetry of 1D hexagonal quasicrystal and its linear piezoelectricity effect, 1D hexagonal quasicrystal control equations of anti-plane problem are derived. Applying Cauchy integral formula, the analytical expressions for the crack tip filed intensity factors are presented with the assumption that the crack are electrical impermeable and electrical permeable. With the variation of the hole-size and the crack length, some of the new model of crack are obtained. In the absence of the electric load, the results match with the classical ones. The numerical results indicate the effects of geometric parameters on the field intensity factors. It is verified that the horizontal crack length and the circle radius can easily promote crack growth. Research on such issues will provide reliable theoretical value for the engineering materials preparation and application.  Related Articles | Metrics

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Fuzzy Robust $H_\infty$ Control for Uncertain Nonlinear Systems via Output Feedback QU Zi-fang, DU Zhen-bin 2016, 33 (2):  199-205.  doi: 10.3969/j.issn.1005-3085.2016.02.009 Abstract ( 37 )   PDF (116KB) ( 3 )   Save This paper is concerned with a fuzzy robust $H_\infty$ control problem via output feedback for a class of uncertain nonlinear systems. The uncertain nonlinear systems are represented by fuzzy Takagi-Sugeno (T-S) model, and a fuzzy controller is designed based on the state observer. A sufficient condition for the existence of fuzzy controller is given in terms of the linear matrix inequalities (LMIs) and the adaptive law. Based on Lyapunov stability theorem, the proposed fuzzy control scheme such that the desired H∞ performance is achieved in the sense that all the closed-loop signals are uniformly ultimately bounded (UUB). Simulation results indicate the effectiveness of the developed control scheme. In this paper, a less conservative fuzzy tracking controller is proposed, where the matching condition and the upper bound are avoided. Comparing with the existing works, the dimension of the LMIs of this paper is reduced. Related Articles | Metrics

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Oscillation Criteria for Third-order Nonlinear Neutral Dynamic Equations on Time Scales ZHANG Zhi-yu, HAN Qiang, YU Yuan-hong 2016, 33 (2):  206-220.  doi: 10.3969/j.issn.1005-3085.2016.02.010 Abstract ( 19 )   PDF (142KB) ( 11 )   Save Many practical problems, such as those from electronic engineering, mechanical engineering, ecological engineering, aerospace engineering and so on, need to be described by dynamic equations on time scales, so it is important in theory and practical significance to study these equations. In this paper, the oscillation and asymptotic behavior of third-order nonlinear neutral delay dynamic equations on time scales are studied by using generalized Riccati transformation technique, integral averaging methods and comparison theorems. The main purpose of this paper is to establish some new oscillation criteria for such dynamic equations. The new Kamenev criteria and Philos criteria are given, and an example is considered to illustrate our main results. Related Articles | Metrics