二参数平稳随机事件流的若干结果

讨论二参数平衡无后效随机事件流的基本性质，局部鞅性和各种二参数Markov性，并用比较简单的方法给出二参数平稳无后效随机事件流的母函数的一般形式。     

二参数有限随机事件流

本文讨论二参数无后效有限随机事件流的鞅性和各种二参数Ｍａｒｋｏｖ性。     

盈余过程的马氏性与索赔到达间隔分布为离散型的连续时间风险模型

本文研究广泛的一类连续时间风险模型盈余过程的马氏性,得到了盈余过程成为马氏过程的充分必要条件．首次建立了索赔到达间隔为离散型分布的连续时间风险模型．并对两个基本特例得到了破产概率的准确表达式．     

一类推广的复合Poisson-Geometric相依风险模型的破产概率

研究了一类推广的复合Poisson—Geometric风险相依模型．利用盈余过程的鞅性,得到了破产概率公式以及破产概率所满足的积分方程和Cramer—Lundberg逼近．最后给出了索赔额服从指数分布时Cramer-Lundberg逼近的精确表达式．     

带干扰的多复合风险模型的盈余首达给定水平的时间分析

对保费收入是复合Poisson过程、理赔含有多个相关险种的带干扰的风险模型盈余首达时间进行研究.首先,对新模型的性质进行了讨论,得到其盈利过程的平稳增量性;其次,基于鞅理论,对风险模型下盈余首次达到给定水平的时间进行了研究.最后,得到了首达时刻的矩母函数以及相应的期望、二阶和三阶中心矩的解析表达式.     

带干扰的一类相依风险模型

本文将古典风险模型推广为带干扰的一类相依风险模型。在此风险模型中,保单到达过程为一Pois-son过程,而索赔到达过程为保单到达过程的P-稀疏过程。利用鞅的方法得到了破产概率和Lundberg不等式。     

保险费收取次数为泊松过程下的广义复合泊松风险模型

经典的破产模型是假定保险公司按单位时间常数速率收取保险费，盈余过程{R（t），t≥0中的S（f）=∑i=1^N（t）Y,为一复合泊松过程，本文将保费到达过程推广为一个Poisson过程，同时将S（t）推广为一个广义复合Poisson过程．针对此模型给出了盈余过程的一些性质，得到关于破产概率的一个定理．     

半鞅及其临界停时

本文讨论Ｂ－值Ｒ．Ｒ．Ｃ过程Ｗ的半鞅性及其与临界停时之间的关系，同时给出相应的临界停时的构作方法，并证明过程Ｗ为非半鞅的特征为Ｐ（＜∞）＞０．本文最后讨论两类矢值过程，它们具有一个Ｒ－控制过程，但不为半鞅．     

复合二项模型下盈余到达一给定水平的时间分析

利用鞅论的方法得到了复合二项模型中盈余过程首次和末次到达一给定水平的时间的分布特征,并导出了几个概率等式,另外,也讨论了其它一些相关量的概率特征.     

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.     

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.     

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。     

American put options with a finite set of exercisable time epochs

The ordinary American put option assumes that investors can exercise their right at any time epoch. However, due to limitations in actual trades, they are not totally free to exercise in time. In this paper, motivated by this practical situation, we consider American put options with a finite set of exercisable time epochs. Assuming that the underlying stock price process follows a discrete-time Markov process, the put option premium is derived. It is shown that, as for the ordinary American put, the option premium is decomposed into the corresponding European put premium plus the early exercise premium under the stationary independent increments assumption. Moreover, the option premium converges to the ordinary American put premium from below as the number of exercisable time epochs increases under regularity conditions. Some lower bound of the option premium is also obtained.     

Steady state of loss systems with a superposition of inputs

The total input of a loss system consisting of a finite number of fully available, identical servers is assumed to be a superposition of a finite number of partial traffic streams, which need not be independent and which are represented by a random marked point process. This paper derives existence, uniqueness and ergodic statements for the steady state of the system at several observation points, i.e. at an arbitrary point in time and at the arrival instants of calls belonging to a fixed partial stream.     

Weak convergence of hilbert valued martingale measures

In this paper, we discuss the property of Hilbert valued martingale measure and introduce the concept of convergence of martingale measures in distribution. The sufficient. and necessary conditions are provided for strongly orthogonal martingale measures with independent increments (Theorem 2.2). The conditions are given for convergence of martingale measures     

First crossing time,overshoot and Appell–Hessenberg type functions

We consider a general insurance risk model with extended flexibility under which claims arrive according to a point process with independent increments, their amounts may have any joint distribution and the premium income is accumulated following any non-decreasing, possibly discontinuous, real valued function. Point processes with independent increments are in general non-stationary, allowing for an arbitrary (possibly discontinuous) claim arrival cumulative intensity function which is appealing for insurance applications. Under these general assumptions, we derive a closed form expression for the joint distribution of the time to ruin and the deficit at ruin, which is remarkable, since as we show, it involves a new interesting class of what we call Appell–Hessenberg type functions. The latter are shown to coincide with the classical Appell polynomials in the Poisson case and to yield a new class of the so called Appell–Hessenberg factorial polynomials in the case of negative binomial claim arrivals. Corollaries of our main result generalize previous ruin formulas e.g. those obtained for the case of stationary Poisson claim arrivals.     

On a New Shot Noise Process and the Induced Survival Model

Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed.