一类带干扰且Cox相关的双险种风险模型

在带有随机扰动的环境中,考虑保单到达及索赔到达均为Cox点过程且两类索赔到达过程相关的一类双险种风险模型.利用鞅技巧,将破产概率的指数上界推广到了更一般的情形.     

一类相依风险模型的破产问题

研究了一类相依的双险种风险模型,其中第一类险种的索赔到达计数过程为E lang(2)过程,第二类险种的索赔到达计数过程为其p-稀疏过程.首先通过更新论证的方法得到罚金折现期望满足的积分-微分方程,然后推导拉普拉斯变换的表达式,并就索赔额服从指数分布的情形得到了罚金折现期望的精确表达式.     

一类Cox风险模型的Gerber-Shiu平均折现罚函数

本文考虑索赔次数到达过程是一类Cox过程的风险模型中的Gerber-shiu平均折现罚函数,建立该函数所满足的积分-微分方程,得出两状态下索赔量分布函数属于K_n-类时破产时间函数的具体表达式.     

一类相依双险种风险模型的罚金折现期望函数

考虑索赔到达具有相依性的一类双险种风险模型,其中第一类险种的索赔计数过程为Poisson过程,第二类险种的索赔计数过程为其p-稀疏过程与广义Erlang(2)过程的和,利用更新论证得到了此风险模型的罚金折现期望函数满足的微积分方程及其Laplace变换的表达式.并就索赔额均服从指数分布的情形,给出了罚金函数及破产概率的精确表达式.     

时间相依更新风险模型中无限时绝对破产概率的渐近性

本文考虑了两类时间相依且带常利率和常值保费收入率的更新风险模型的无限时绝对破产概率, 其中索赔额及其到达时间间隔构成独立同分布的随机对列, 以及每个随机对遵循某种相依结构. 基于此, 当索赔额分布属于R_-∞∩J(γ), γ > 0 分布族时, 我们分别得到了两类时间相依结构下的无限时绝对破产概率的渐近公式和渐近上界.     

重尾索赔下的一类相依风险模型的若干问题

本文研究了重尾索赔下的一类相依风险模型,得到了破产概率的尾等价式及索赔盈余过程大偏差的渐近关系式.在该模型中,一索赔到达过程是Poisson过程,另一索赔到达过程为其p-稀疏过程.     

具有常红利边界和延迟索赔的一类离散更新风险模型

考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子.     

广义负相依一般风险模型中有限时破产概率的估计及数值模拟

本文研究了一类带利率的重尾相依风险模型, 其中索赔额是一列上广义负相依随机变量, 索赔到达过程是一般的非负整值过程, 并且独立于索赔额序列, 保费收入过程是一个一般的非负非降随机过程. 我们考虑了两种情况, 其一是索赔额、索赔到达过程及保费收入过程相互独立, 其二是累积折现保费收入总量的尾概率可以被索赔额的尾概率高阶控制, 得到了保险公司有限时破产概率的渐近估计,并且给出了相应的数值模拟, 验证了理论结果的合理性.     

具有两类索赔相关风险过程的罚金折现函数

考虑两类索赔相关风险过程.两类索赔计数过程分别为独立的Poisson和广义Erlang(2)过程.将该过程转换为两类独立索赔风险过程,得到了该过程的罚金折现函数满足的积分微分方程及该函数的拉普拉斯变换的表达式,且当索赔额服从指数分布时,给出了罚金折现函数及破产概率的表达式.     

一类考虑破产限的双险种风险模型

本文研究一类考虑破产限的双险种风险模型,其中,一类险种保单到达是强度为λ的Poisson过程,退保、保单的非正常索赔以及正常索赔过程分别是关于保单到达过程的ρ_1—稀疏过程、ρ_2—稀疏过程、ρ_3—稀疏过程,另一类险种保单到达及索赔均服从复合负二项分布,运用鞅方法讨论该模型盈余过程的性质,并给出最终破产概率的表达式和Lundberg不等式.     

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.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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].