中国科学院数学与系统科学研究院期刊网

2018年, 第34卷, 第3期　刊出日期：2018-07-15
  

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    Original Articles
  • An Actuarial Approach to Reload Option Valuation for a Non-tradable Risk Assets under Jump-diffusion Process and Stochastic Interest Rate
    Cong-cong XU, Zuo-liang XU
    应用数学学报(英文版). 2018, 34(3): 451-468. https://doi.org/10.1007/s10255-018-0759-5
    摘要 ( ) PDF全文   可视化   收藏

    We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.

    • ARTICLES
  • Lie Point Symmetry Analysis of the Harry-Dym Type Equation with Riemann-Liouville Fractional Derivative
    Li-zhen WANG, Ding-jiang WANG, Shou-feng SHEN, Qing HUANG
    应用数学学报(英文版). 2018, 34(3): 469-477. https://doi.org/10.1007/s10255-018-0760-z
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, Lie point symmetry group of the Harry-Dym type equation with Riemann-Liouville fractional derivative is constructed. Then complete subgroup classification is obtained by means of the optimal system method. Finally, corresponding group-invariant solutions with reduced fractional ordinary differential equations are presented via similarity reductions.
  • A Note on Directed Genera of Some Tournaments
    Jian-bing LIU, Rong-xia HAO
    应用数学学报(英文版). 2018, 34(3): 478-484. https://doi.org/10.1007/s10255-018-0763-9
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can be directed embedded. Bonnington, Conder, Morton and McKenna[J. Combin. Theory Ser. B, 85(2002) 1-20] gave the problem that which tournaments on n vertices have the directed genus ⎡((n-3)(n-4))/12⎤, the genus of Kn. In this paper, we use the current graph method to show that there exists a tournament, which has the directed genus ⎡((n-3)(n-4))/12⎤, on n vertices if and only if n ≡ 3 or 7 (mod 12).
  • The Solutions of the Coupled Einstein-Maxwell Equations and Dilaton Equations
    Rui-feng ZHANG, Ya GU
    应用数学学报(英文版). 2018, 34(3): 485-492. https://doi.org/10.1007/s10255-018-0764-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.
  • A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line
    Ning ZHANG, Tie-cheng XIA, En-gui FAN
    应用数学学报(英文版). 2018, 34(3): 493-515. https://doi.org/10.1007/s10255-018-0765-7
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation
    i∂tu + ∂xxu-i|u|2∂xu=0
    on the half line (-∞, 0] with decaying initial value. Assuming that the solution u(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit (x, t) dependence and is given in terms of the spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which are obtained from the initial data u0(x)=u(x, 0) and the boundary data g0(t)=u(0, t), g1(t)=ux(0, t), respectively. The spectral functions are not independent, but satisfy a so-called global relation.
  • Nonlinear Least Squares Estimation of Log-ACD Models
    Zhao CHEN, Wei LIU, Christina Dan WANG, Wu-qing WU, Yao-hua WU
    应用数学学报(英文版). 2018, 34(3): 516-533. https://doi.org/10.1007/s10255-018-0766-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration (Log-ACD) model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.
  • On the Motion of Shear-Thinning Heat-Conducting Incompressible Fluid-Rigid System
    Ya-zhou CHEN, Qiao-lin HE, Xiao-ding SHI, Teng WANG, Xiao-ping WANG
    应用数学学报(英文版). 2018, 34(3): 534-552. https://doi.org/10.1007/s10255-018-0767-5
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.
  • The Finite-time Ruin Probability of a Discrete-time Risk Model with Subexponential and Dependent Insurance and Financial Risks
    Shi-jie WANG, Chuan-wei ZHANG, Xue-jun WANG, Wen-sheng WANG
    应用数学学报(英文版). 2018, 34(3): 553-565. https://doi.org/10.1007/s10255-018-0768-4
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Consider a discrete-time risk model with insurance and financial risks in a stochastic economic environment. Assume that the insurance and financial risks form a sequence of independent and identically distributed random vectors with a generic random vector following a wide type of dependence structure. An asymptotic formula for the finite-time ruin probability with subexponential insurance risks is derived. In doing so, the subexponentiality of the product of two dependent random variables is investigated simultaneously.
  • Global Well-posedness of the Stochastic Generalized Kuramoto-Sivashinsky Equation with Multiplicative Noise
    Wei WU, Shang-bin CUI, Jin-qiao DUAN
    应用数学学报(英文版). 2018, 34(3): 566-584. https://doi.org/10.1007/s10255-018-0769-3
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Global well-posedness of the initial-boundary value problem for the stochastic generalized Kuramoto-Sivashinsky equation in a bounded domain D with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data u0 ∈ L2(D×Ω), this problem has a unique global solution u in the space L2(Ω, C([0, T], L2(D))) for any T > 0, and the solution map u0 ↦ u is Lipschitz continuous.
  • Empirical Likelihood for Varying Coefficient EV Models under Longitudinal Data
    Qiang LIU
    应用数学学报(英文版). 2018, 34(3): 585-596. https://doi.org/10.1007/s10255-018-0770-x
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated. An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.
  • Scheduling Reclaimer Operations in the Stockyard to Minimize Makespan
    Chao WANG, Xi-wen LU, René SITTERS
    应用数学学报(英文版). 2018, 34(3): 597-609. https://doi.org/10.1007/s10255-018-0758-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper considers a reclaimer scheduling problem in which one has to collect bulk material from stockpiles in the quay in such a way that the time used is minimized. When reclaimers are allowed to work on the same stockpile simultaneously, a fully polynomial time approximation scheme (FPTAS) is designed. Further, we present a 2-approximation algorithm in the case that any stockpile can be handled by only one reclaimer at a time. When the number of reclaimers is two, we give a 3/2-approximation algorithm. Numerical experiments show that the algorithms perform much better than our worst case analysis guarantees.
  • Analysis of Topological Structure in Transiently Chaotic Neural Networks
    Yang GAO, Zuo-huan ZHENG
    应用数学学报(英文版). 2018, 34(3): 610-621. https://doi.org/10.1007/s10255-018-0771-9
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.
  • Representation Theorem for Generators of Quadratic BSDEs
    Shi-qiu ZHENG, Shou-mei LI
    应用数学学报(英文版). 2018, 34(3): 622-635. https://doi.org/10.1007/s10255-018-0772-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.
    • Original Articles
  • Neighborhood Conditions for Fractional ID-k-factor-critical Graphs
    Si-zhong ZHOU, Zhi-ren SUN
    应用数学学报(英文版). 2018, 34(3): 636-644. https://doi.org/10.1007/s10255-018-0773-7
    摘要 ( ) PDF全文 ( )   可视化   收藏

    Let G be a graph and k ≥ 2 a positive integer. Let h:E(G) →[0, 1] be a function. If  holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh={e ∈ E(G):h(e) > 0}. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical), if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n ≥ 9k-14 and for any subset X⊂V(G) we have

    then G is fractional ID-k-factor-critical.

    • ARTICLES
  • Research on the Efficient Computation Mechanism-in the Case of N-vehicle Exploration Problem
    Fang YU, Jin-chuan CUI
    应用数学学报(英文版). 2018, 34(3): 645-657. https://doi.org/10.1007/s10255-018-0774-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The research of efficient computation focus on special structures of NP-hard problem instances and request providing reasonable computing cost of instances in polynomial time. Based on the theory of combinatorial optimization, by studying the clusters partition and the clusters complexity measurement in Nvehicle exploration problem, we build a frame of efficient computation and provide an application of tractability for NP-hard problem. Three N-vehicle examples show that when we use efficient computation mechanism on N-vehicle, through polynomial steps of tractability analysis, decision makers can get the computing cost of searching optimal solution before practical calculation.
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