带有风险回避的最优消费模型研究

本文在文献[1]和[2]的基础上,把模型参数推广为时间t的变量,折扣因子β(t)为[0,T]上的有界可测函数,通过计算得出带有风险回避的最优消费条件和投资公式.     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下, 保费收入为复合Poisson 过程, 理赔到达过程为一般更新过程的风险模型. 利用离散化的方法, 获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式, 推广了文[1] 和文[2] 中的相关结果.     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下,保费收入为复合Poisson过程,理赔到达过程为一般更新过程的风险模型.利用离散化的方法,获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式,推广了文[1]和文[2]中的相关结果.     

一类离散风险模型的盈余极值的联合分布

本文研究了一类离散风险模型,利用[1]和[2]关于古典风险模型的结论,得到了该风险过程在破产前和最后一次返回零点前公司盈余的极大值和极小值的联合分布,推广到了保费收入过程依赖于保单计数过程的情况.     

复合索赔次数模型与混合索赔次数模型中的若干结果

本文利用完整描述方法研究复合索赔次数模型与混合索赔次数模型中总索赔次数的概率分布 ,得到了十余例典型索赔次数模型的相关结果 ,这些结果推广了文献 [1]、[2 ]、[6 ]的有关结论。     

一类半线性反应对流扩散模型的特征差分方法和分析

1.引 言如下形式的半线性反应对流扩散方程组分别在生命科学、化学和环境科学中,有大量的应用模型[1-3].其中文献[2-6]分别讨论了方程组(1.1)的各种特殊模型的定性性质.文献[6]讨论了一类线性模型的流线扩散有限元分析.作者在文[7]中,分别利用标准有限元方法和交替方向有限元方法,对(1.1)的一些特殊情形作了数值分析.     

一类平稳的奇异性随机控制问题的研究

§1.引言 关于奇异型随机控制问题,已有很多文章进行研究,如文献[1]—[3]等。在某种意义上来说,文献[2]的结果比文献[1]更为一般。具体描述如下: 设W_t,t≥0为概率空间(Ω,(?),P)上标准Wiener过程。(?)_t为由此过程所生成的上升σ-域族。以(?)表(?)_t适应左连续零初值有限变差过程的全体。对,有正规分解表全变差过程。我们所说的控制全包含在集中。文献[2]研究的平稳模型是:     

一个复合风险模型的引入及其大偏差估计的建立

本文研究了关于独立随机和精大偏差的估计问题,改进了文献[4,7]的结果。首先我们引入了一个比过去工作更现实复合更新风险模型,然后在该模型下建立了与文献中完全相同的精大偏差结果。     

GlueVaR失真风险度量下的最优再保险（英文）

受到文献[1]和文献[2]的启发,本文从保险人的角度,研究了GlueVaR失真风险度量下的最优再保险问题.假设保险标的的损失为X,保险人为分散风险签订了以索赔总额为计算基础的分保合同.按合同,分保人承担的风险为f(X),保险人承担剩下的风险X-f(X).此外基于期望保费原则,保险人需支付分保人再保险费(1+ρ)E[f(X)](其中ρ为安全负载系数).采用文献[2]中的技术方法,我们得出此时最优转移损失函数是一类增凸函数.从而可知最优再保险策略为停止损失再保险.     

一类相依两险种风险模型的分类破产概率

本文考虑文[1]中引入的一类索赔达到计数过程相关的两险种风险模型.利用更新方法,获得了该风险模型的分类破产概率的渐进结果,并给出了指数索赔情形下分类破产概率的表达式,从而改进了文[1]中的相关结果.     

半相依模型参数估计的改进

对于m个半相依回归系统的未知回归系数, 文献[7]提出一种利用信息逐次迭加的方法, 该文首先在其基础上给出一种进一步改进形式, 并得到了其相合性, 同时作者借鉴文献[7]提出逐次迭加信息的构造估计思想给出一种具有小样本优良性的可行估计, 模拟研究也表明作者的改进估计是有效的.文献[10]根据Rao的协方差改进思想, 给出一种更为简洁的两步估计, 该文在此估计基础上给出一种改进形式, 新估计具有更好的可操作性和均方误差意义下的优良性.     

Diffusion in Glassy Polymers: Sorption of a Finite Amount of Solvent

A family of 1-D moving boundary models describing the diffusion of a finite amount of a penetrant in a glassy polymer is studied. Local existence of a unique classical solution is obtained for a generic quasilinear model. Specific data are then chosen which can be found in the literature (cf. [6]) and global existence of the classical solution and its convergence to an equilibrium solution are proven. Finally a rigorous proof is provided for a formal perturbation argument proposed in [6] and used therein to estimate the rate of convergence of the solution towards the equilibrium.     

网络割的计数

指出了文献[1],[2]所出现的欠妥处,给出了网络割的计数.     

GRAPHIC EXTENSIONS OF MAPPINGS

ABSTRACT

Given a mapping f: X → Y and an extension e: X → [Xtilde] of X, the restriction of the projection Π: [Xtilde] X Y → Y to the closure of the graph of f in [Xtilde] X Y is called the graphic extension of f with respect to e. It is shown that this approach is widely applicable to various types of topological extensions of mappings found in the literature and often gives simpler proofs of their existence, properties, and results relating to them.     

A note on stochastic semilinear equations and their associated Fokker–Planck equations

The main purpose of this paper is to prove existence and uniqueness of (probabilistically weak and strong) solutions to stochastic differential equations (SDE) on Hilbert spaces under a new approximation condition on the drift, recently proposed in [6] to solve Fokker–Planck equations (FPE), extended in this paper to a considerably larger class of drifts. As a consequence we prove existence of martingale solutions to the SDE (whose time marginals then solve the corresponding FPE). Applications include stochastic semilinear partial differential equations with white noise and a non-linear drift part which is the sum of a Burgers-type part and a reaction diffusion part. The main novelty is that the latter is no longer assumed to be of at most linear, but of at most polynomial growth. This case so far had not been covered by the existing literature. We also give a direct and more analytic proof for existence of solutions to the corresponding FPE, extending the technique from [6] to our more general framework, which in turn requires to work on a suitable Gelfand triple rather than just the Hilbert state space.     

EXISTENCE OF LIMIT CYCLES FOR QUADRATIC SYSTEMS WITH ONE INFINITE SINGULAR POINT

This paper discusses the existence of limit cycles for quadratic systems with one infinite singular point. In particular, the author gives necessary anal sufficient conditions for the existence of a unique limit cycle of a class of quadratic systems with an integral line under certain conditions. As a special consequence, all the results of [-6] and [7] can be implied by means of affine transformations. The method used here is much simpler than those of [6] and [7].     

A generalization of results of P. Erdös,G. Katona,and D. J. Kleitman concerning Sperner's theorem

A result of Sperner [1] determining the maximal number of subsets of a given set, such that no one is included in the other, has been generalized and strengthened modifying the restrictive condition by Erdös [2], by Katona [3], and Kleitman [7], and by others [4, 5]. A different kind of generalization has been obtained by de Bruijn, Tenbergen, and Kruywijk [6] using the same restrictive condition but for more general entities than sets, namely, for systems in which the elements may occur more than once. That approach is fundamental for number-theoretical considerations since the totality of prime divisors of a given number (each considered with its multiplicity) is of that nature. In this paper we will generalize the results of [2] and [3, 7] in the sense of [6].     

FINITE ELEMENT ANALYSIS OF A LOCAL EXPONENTIALLY FITTED SCHEME FOR TIME-DEPENDENTCONVECTION-DIFFUSION PROBLEMS

1.IntroductionConsiderthetime-dependentconvection-diffusionproblemat--Euzx a(x,t)u. b(x,t)u~f(x,t),(x,t)E[0,1]x[0,T](1.1)u(0,t)=u(1,t)~0,tE[0,T].(1.2)u(x,0)=u000,xE[0,1],(1.3)a(x,t)2or>0,(1.4)b(x,t)--a.(x,t)/220>0,(1.5)where0SE<<1'(1.1)-(1.5)canbereg...     

sum from n=1 to +∞(1/n~(2m))的初等解法

本文用初等的方法研究sum from n=1 to(1/n~(2m))(m∈N)的求和问题。这个问题最先由Euler[8]解决。文献[1][6]给出了另两种求解方法。特别地,对于m=1的情形,即sum from n=1 to ∞(1/n~2)=((π~2)/6),已有许多不同的证明方法,可见文献[2][3][4][5]以及那里的参考文献。本文的想法,主要受文献[5][6]的启发而来的。     

A relation between the output regulation and the observer design for nonlinear systems

Output regulation and observer design are two important problems for nonlinear systems, and there is a vast literature addressing each problem separately in the control literature. Isidori and Byrnes [1] have solved the output regulation problem for nonlinear systems with a Poisson stable exosystem, and Sundarapandian [2] has solved the exponential observer design problem for Lyapunov stable nonlinear systems. In this paper, we demonstrate that for a special class of Lyapunov stable nonlinear systems, namely neutrally stable systems, the exponential observer design problem can be solved by converting it into an output regulation problem and then solving the new problem using the output regulation techniques of Isidori and Byrnes [1]. Finally, we present the corresponding results for the discrete-time case.