15 October 2010, Volume 26 Issue 4
    

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  • 论文
    Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models
    G. Yin, Zhuo Jin, Hailiang Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 529-542.
    DOI:10.1007/s10255-010-0023-0
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin. Compound Poisson processes with regime switching are used to model the surplus and the switching (a continuous-time controlled Markov chain) represents random environment and other economic conditions. Assuming the switching to be fast varying together with suitable conditions, it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain. Under simple conditions, the optimal policy of the limit dividend strategy is a threshold policy. Using the optimal policy of the limit system as a guide, feedback control for the original surplus is then developed. It is demonstrated that the constructed dividend policy is asymptotically optimal.

  • 论文
    Convergence of a Non-interior Continuation Algorithm for the Monotone SCCP
    Nan Lu, Zheng-Hai Huang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 543-556.
    DOI:10.1007/s10255-010-0024-z
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    It is well known that the symmetric cone complementarity problem (SCCP) is a broad class of optimization problems which contains many optimization problems as special cases. Based on a general smooth- ing function, we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP. The proposed algorithm solves at most one system of linear equations at each iteration. By using the theory of Euclidean Jordan algebras, we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.

  • 论文
    A Property of g-probabilities
    Dong-mei Guo, Zeng-jing Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 567-574.
    DOI:10.1007/s10255-010-0021-2
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    Most work on capacities has focused on the 2-alternating and sub 2-alternating. In this paper we consider the capacities-g-probabilities derived from peng's g-expectations. When g satisfies some conditions, we show that the g-probabilities fail to be 2-alternating but are sub 2-alternating.

  • 论文
    The Gerber-Shiu Expected Discounted Penalty Function for Lévy Insurance Risk Processes
    Xiang-hua Zhao, Chuan-cun Yin
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 575-586.
    DOI:10.1007/s10255-010-0025-y
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we study a general Lévy risk process with positive and negative jumps. A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model. We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.

  • 论文
    Strong Approximations for a Kumar-Seidman Network under a Priority Service Discipline
    Lin Wu, Chuan-xi Zhu, Yun-jiang Wu
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 587-596.
    DOI:10.1007/s10255-010-0026-x
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we derive the strong approximations for a four-class two station multi-class queuing network (Kumar-Seidman network) under a priority service discipline. Within a group, jobs are served in the order of arrival, that is, a first-in-first-out disciple, and among groups, jobs are served under a pre-emptiveresume priority disciple. We show that if the input data (i.e., the arrival and service processe) satisfy an approximation (such as the functional law-of-iterated logarithm approximation or the strong approximation), the output data (the departure processes) and the performance measures (such as the queue length, the work load and the sojourn time process ) satisfy a similar approximation.

  • 论文
    Profiles of Blow-up Solutions for the Gross-Pitaevskii Equation
    Shi-hui Zhu, Jian Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 597-606.
    DOI:10.1007/s10255-010-0027-9
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    This paper is concerned with the blow-up solutions of the Cauchy problem for Gross-Pitaevskii equation. In terms of Merle and Raphaël's arguments as well as Carles' transformation, the limiting profiles of blow-up solutions are obtained. In addition, the nonexistence of a strong limit at the blow-up time and the existence of L2 profile outside the blow-up point for the blow-up solutions are obtained.

  • 论文
    Some Results on Spanning Trees
    Bing Yao, Zhong-fu Zhang, Jian-fang Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 607-616.
    DOI:10.1007/s10255-010-0011-4
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    Some structures of spanning trees with many or less leaves in a connected graph are determined. We show (1) a connected graph G has a spanning tree T with minimum leaves such that T contains a longest path, and (2) a connected graph G on n vertices contains a spanning tree T with the maximum leaves such that Δ(G) = Δ(T) and the number of leaves of T is not greater than n-D(G) + 1, where D(G) is the diameter of G.

  • 论文
    Asymptotic Property of Approximation to xαsgn x by Newman Type Operators
    Qian Zhan, Shu-sheng Xu, Yue-hong Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 617-624.
    DOI:10.1007/s10255-007-7147-x
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    Approximation to the function |x| plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals |x| if α = 1. We construct a Newman Type Operator rn(x) and prove

  • 论文
    A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals
    Hu Yang, Yuan-yuan Hao
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 625-632.
    DOI:10.1007/s10255-010-0028-8
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we consider a generalization of the classical ruin model, where the income is random and the distribution of the time between two claim occurrences depends on the previous claim size. This model is more appropriate than the classical ruin model. Explicit expression for the generating function of the Gerber- Shiu expected discounted penalty function are derived. A similar model is discussed. Finally, the result are showed by two examples.

  • 论文
    Attractors for Discrete Nonlinear Schrödinger Equation with Delay
    Tao Chen, Sheng-fan Zhou, Cai-di Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 633-642.
    DOI:10.1007/s10255-007-7101-y
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    In this paper, we first prove the existence of the global attractor Av∈C([-v, 0], e2) (-v > 0) for a weak damping discrete nonlinear Schrodinger equation with delay. Then we consider an upper semi-continuity of Av as v→ 0+.

  • 论文
    The Stability of Traveling Waves with Non-critical Speeds for Some Competition Systems
    Ye Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 643-652.
    DOI:10.1007/s10255-010-0029-7
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    This paper is concerned with some quasilinear cross-diffusion systems which model competing species in mathematical ecology. By detailed spectral analysis, each traveling wave solution with non-critical speed is proved to be locally exponentially stable to perturbations in some exponentially weighted spaces.

  • 论文
    Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure
    Luo-gen Yao, Gang Yang, Xiang-qun Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 653-660.
    DOI:10.1007/s10255-010-0030-1
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    The Moore-Penrose inverse is an important tool in algebra. This paper shows that the Moore- Penrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition. We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable. Furthermore, we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse. Specifically, the minimal martingale measure in a generalized Black-Scholes model is found.

  • 论文
    Smoothness of Certain Functions in Two Kinds of Risk Models with a Barrier Dividend Strategy
    Wei Wang, Jing-min He, Rong Wu
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 661-668.
    DOI:10.1007/s10255-010-0016-z
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy. Mainly using technique from the piecewise deterministic Markov processes theory, we prove that the function is continuously differentiable in the first risk model. Using the weak infinitesimal generator method of Markov processes, we prove that the function is twice continuously differentiable in the second risk model. Intego-differential equations satisfied by them are derived.

  • 论文
    Application of Exp-function Method to Generalized Burgers-Fisher Equation
    Zhen-hui Xu, Da-quan Xian
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 669-676.
    DOI:10.1007/s10255-010-0031-0
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    In this paper, the Exp-function method is used to construct exact solitary wave solutions for the generalized Burgers-Fisher equation with nonlinear terms of any order. With the aid of Maple computation, we obtain many new and more general exact solitary wave solutions expressed by various exponential and hyperbolic functions. Our results can successfully recover previously known solitary wave solutions that have been found by the tanh-function method and other more sophisticated methods.

  • 论文
    Bifurcations of Resonant Solutions and Chaos in Physical Pendulum Equation with Suspension Axis Vibrations
    Xiang-ling Fu, Jin Deng, Jian-ping Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(4): 677-704.
    DOI:10.1007/s10255-010-0032-z
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    This paper is a continuation of “Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations”. In this paper, we investigate the existence and the bifurcations of resonant solution for ω0 : ω : Ω ≈ 1 : 1 : n,1 : 2 : n,1 : 3 : n,2 : 1 : n and 3 : 1 : n by using second-order averaging method, give a criterion for the existence of resonant solution for ω0 : ω : Ω ≈ 1 : m : n by using Melnikov’s method and verify the theoretical analysis by numerical simulations. By numerical simulation, we expose some other interesting dynamical behaviors including the entire invariant torus region, the cascade of invariant torus behaviors, the entire chaos region without periodic windows, chaotic region with complex periodic windows, the entire period-one orbits region; the jumping behaviors including invariant torus behaviors converting to period-one orbits, from chaos to invariant torus behaviors or from invariant torus behaviors to chaos, from period-one to chaos, from invariant torus behaviors to another invariant torus behaviors; the interior crisis; and the different nice invariant torus attractors and chaotic attractors. The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations. It exhibits many invariant torus behaviors under the resonant conditions. We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations. However, we did not find the cascades of period-doubling bifurcation.

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