离散时间的双Poisson模型的破产概率

本文在离散复合Poisson风险模型的基础上,研究保费的收取也为一个Poisson过程的模型, 在保费收取量和理赔量都离散取整数值时,我们运用转移概率推导出了保险公司在有限时间内破产的概率以及最终破产概率的级数表达式和矩阵表达式.     

带常利率的双Poisson模型的破产概率

本文在保费的收取和理赔都为复合Poisson过程的盈余过程的基础上,考虑盈余产生利息的双Pois-son模型,在保费收取量和理赔量都取整数值时,我们运用转移概率推导出了破产概率的近似计算公式及误差估计式,并且得到了破产概率的一个上界和一个下界.     

保费收取过程是随机过程的双险种风险模型

研究保费收取过程是一个随机过程的双险种风险模型,得出了Lundberg上界、最终破产概率、不破产所满足的微积分方程、索赔服从指数分布的不破产概率、有限时间不破产所满足的微积分方程.     

保险系统中一种推广风险模型的破产概率

将经典复合 Poisson风险模型推广至更为一般情况 ,其中保单以 Poisson分布流到达且收取的保费为随机变量 ,建立一种双复合 Poisson风险模型 .对此模型 ,得到了最终破产概率的一般表达式和破产概率的一个上界估计值 .     

双复合Poisson风险模型

研究了保费收取过程是复合Po isson过程,索赔总额是复合Po isson过程的风险模型,给出了不破产概率的积分表示,以及在特殊情况下不破产概率的具体表达式,并用鞅方法得出了破产概率满足的Lundberg不等式和一般公式.     

一类带干扰索赔相关风险模型的破产概率

讨论一类带干扰索赔相关且保费收取为一复合泊松过程风险模型的破产问题，利用鞅方法得出Lundberg不等式和最终破产概率公式。     

广义二元复合二项风险模型的破产概率

本文研究了索赔过程和保费收取次数均为二项分布的双险种风险模型,得到了其破产概率的一般公式。     

保费随机收取下带特殊分红策略的复合二项风险模型

本文讨论保费随机收取情形下带特殊分红策略的复合二项风险模型.考虑当盈余大于或等于一个给定的非负红利界并且索赔不发生时保险公司以一定概率给股东分红,得到该模型的罚金函数的递推公式,然后利用矩阵知识证明其存在唯一解,最后给出破产概率、破产时破产赤字分布概率函数的递推公式.     

带干扰的保费随机收取的双险种风险模型

推广了已有文献中提出的带干扰的双险种复合负二项风险模型,让保费收取次数服从负二项分布,两类险种的索赔也服从负二项分布,得到了带干扰的保费随机收取的双险种风险模型,给出了破产概率的一般表达式和上界．     

索赔到达过程为马氏跳过程的一类风险模型

论将索赔到达点过程由Poisson点过程推广为由马氏链的跳跃点形成的点过程，保费收取由净收入随机确定，我们得到破产概率ψ（u)及条件破产概率φi(u)满足的积分方程．     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.