具有随机保护水平的跳跃扩散模型下的动态基金保护定价

动态基金保护可以确保投资者的基金价格在投资期内不会低于某个投资障碍水平.用两个相关的跳扩散模型来分别刻画动态基金保护的基金价格和障碍水平,利用首中时的Laplace变换给出了超指数跳扩散过程下,动态基金保护价格的Laplace变换的显示表达式.利用Gaver-Stehfest算法,给出了动态资金保护价格的一些数值结果.     

有限图上首达时等随机变量的极限定理

1965年,Hammersley和Welsh在["Bernoulli 1713,Bayes 1763,Laplace 1813",1965,61-110]里提出了首达渗流模型.此后对该模型的研究主要集中于无限图,特别是整数格点Z~d上.近年来一些概率学家开始关注有限图上的首达渗流模型.有限图上首达渗流模型的关注点与无限图上有截然不同,主要涉及首达时、跳数、淹没时、直径等随机变量的极限行为.本文对于有限图上首达渗流模型的首达时等随机变量的极限定理进行了综述.     

一类非线性中立型脉冲时滞微分方程解的渐近性

该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件.     

布朗运动对某些集的首中时分布

首中时是近代马氏过程中的一个重要概念.作为强马氏过程的布朗运动,其首中时在位势理论的 Dirichlet 问题与平衡问题中,都是一个关键性的量.首中时分布函数在上述问题中都处于重要地位。特别,已经证明〔1〕,它是热传导方程在一定初始条件与边值条件下的唯一解。因此,求布朗运动对各种集的首中时分布函数,就成了近代布朗运     

高维布朗运动关于超平面的若干问题

<正> 高维布朗运动中,超平面的首中点分布已见于[1].最近又求出了超平面的首中时分布.本文首先给出用禁止密度表示的超平面首中点与首中时之联合分布;然后由从带域内出发的布朗运动终将离开此带域着手,证明了任一布朗运动必中任一超平面,由此得出布朗运动穿越超平面(及带域)无穷多次的结论;最后研究了首达超平面(及带域)前     

跳扩散模型下可提前违约的脆弱期权定价

该文章利用跳-扩散模型和几何布朗运动模型分别对股票价格和期权空头方资产负债比进行建模.在对违约风险的刻画上选取首达时模型,当资产负债比小于等于一时视为违约发生,并在此假定违约发生时期权立即执行,补偿率为外生随机变量.在跳跃幅度上,该文章给出了服从对数正态以及更一般分布的情况的讨论,同时在对股票的建模和对违约时刻的判断上分别完善了Rich和魏正元的工作,并使用Matlab工具对定价进行实现.     

Brown运动关于球及球面的若干问题 *

给出了从空间任一点出发的Brown运动在球内停留时间的分布与球面首中时分布,也给出了从球内任一点出发的Brown运动末遇球面之前的极大游程与首达极大时的联合分布.     

多维随机过程首中时的强正相依性

研究多维随机过程X^-(t)的首中时的SPD相依结构，拓展了Ebrahimi等关于POD（Positively Orthant Dependent)和作者关于SPOD（Strongly Positively Orthant Dependent)的某些结果。刻划SPD的另一特征，还给出最大无穷可分过程首中时之间的SPD性质及其首中时向量（r1(U1),r2(U2))联合分布的下界（其中Ui是增Borel集，i=1,2)。     

具有正负系数的二阶中立型时滞微分方程的振动性

将研究带有正负系数的的二阶时滞微分方程解的振动性,使用文献中的思想,得到了这类方程振动解存在的充分条件,推广和改进了文献中的相关结论,并且通过具体的例子说明所得结论的优越性.     

中国——最早认识并应用负数的国家

华罗庚说:“数学是中国人民擅长的学科”. 东汉初(公元1世纪),我国第一部有名的数学书《九章算术》中出现了“正负术”.我国魏晋时期著名数学家刘徽为“正负术”作注解释说:“今两算得失相反,要令正负以名之,正算赤,负算黑,否则邪正为异”.这里的“算”是指小竹棒,表示数.注释的大概意思是:两个得失相反的数,要用正负来表示,规定正数用红色小竹棒,负数用黑色小竹棒;若用同色小竹棒的话,则正数正放,负数斜放,用以区别.     

Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries

Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparison of different diffusion models where first passage times represent an important feature and the determination of upper and lower bounds for first passage time distributions.     

On the first passage time of a simple random walk on a tree

We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering the known result that these are integers. A relationship of the mean first passage matrix with the distance matrix is established and used to derive a formula for the inverse of the mean first passage matrix.     

Mean and variance of first passage time of non-homogeneous random walk

The prime concern of this paper is the first passage time of a non-homogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.     

The first passage time density of Ornstein–Uhlenbeck process with continuous and impulsive excitations

The first passage time of the Ornstein–Uhlenbeck process plays a prototype role in various noise-induced escape problems. In order to calculate the first passage time density of the Ornstein–Uhlenbeck process modulated by continuous and impulsive periodic excitations using the second kind Volterra integral equation method, we adopt an approximation scheme of approaching Dirac delta function by alpha function to transform the involved discontinuous dynamical threshold into a smooth one. It is proven that the first passage time of the approximate model converges to the first passage time of the original model in probability as the approximation exponent alpha tends to infinity. For given parameters, our numerical realizations further demonstrate that good approximation effect can be achieved when the approximation exponent alpha is 10.     

Some results on first passage times in one dimensional random walks

Analytic expressions are presented for the characteristic function of the first passage time distribution for biased random walk on a finite chain (and diffusion with drift on a finite line); of the first passage time distribution for a random walk on a chain, in which the events (jumps) are governed by an arbitrary renewal process; and of the distribution of the time of escape from a bounded set of points in the latter case. A fundamental relation between the first passage time distribution and the conditional probability for random walk (or diffusion) in one dimension is analyzed and generalized.     

Directionally Convex Comparison of Correlated First Passage Times

Many important classes of multivariate distributions arising from reliability modeling are the distributions of correlated first passage times of certain multivariate point processes. In this paper, we obtain results that compare variability and dependence structure of these correlated first passage times, in the sense of directionally convex ordering. Under certain conditions, we also obtain some easily computable distributional bounds for the first passage times whose joint distributions can not be expressed explicitly.     

On first passage times of a hyper-exponential jump diffusion process

We investigate some important probabilistic properties relating to the first passage time of a hyper-exponential jump diffusion process, including its finiteness, expectation, conditional memorylessness, and conditional independence. Moreover, the joint distribution of the first passage time and the overshoot is studied from a primal-dual perspective.     

组合分布在求解直线上n步随机游动首次通过问题上的应用

基于组合过程模型给出其轨道对目标集的首次通过概率及首中点的分布函数 ,并由此给出直线上n步随机游动的首次通过概率及首中点分布函数的一类显式 .     

First passage probabilities of one-dimensional diffusion processes

This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.     

First Passage Time for Brownian Motion and Piecewise Linear Boundaries

We propose a new approach to calculating the first passage time densities for Brownian motion crossing piecewise linear boundaries which can be discontinuous. Using this approach we obtain explicit formulas for the first passage densities and show that they are continuously differentiable except at the break points of the boundaries. Furthermore, these formulas can be used to approximate the first passage time distributions for general nonlinear boundaries. The numerical computation can be easily done by using the Monte Carlo integration, which is straightforward to implement. Some numerical examples are presented for illustration. This approach can be further extended to compute two-sided boundary crossing distributions.