关于Primitive布朗运动增量的一些下极限结果

Let {W(t);t≥0} be a standard Brownian motion. For a positive integer m,define a Gaussian process Xm(t)=(1/m!)∫^1 0(t-s)^mdW(s). In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities. Some previous results are extended and improved.     

欧式向上敲出看涨认购权证的鞅方法定价

在普通的认购权证上嵌入障碍期权的特点 ,便会得到一类新型的权证敲出 (敲入 )型认购权证 ,本文以向上敲出看涨认购权证为例 ,先给出它的定义 ,根据该定义 ,以鞅定价方法推导出欧式向上敲出看涨认购权证的封闭解评价模型 ,为实践者提供理论上的参考价格 .     

Functional Modulus of Continuity for Brownian Motion in Holder Norm

The author establishes a large deviation for κ-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Hoelder norm can be obtained.     

一类超扩散过程的概率估计

本文研究了一般椭圆算子对应扩散的支集,给出了一个估计,并推广了文[1]的一个结果。     

指数屏障期权定价模型

本文在股票价格服从几何布朗运动的假设下,采用一种简化的方法,推导了指数屏障期权定价公式。该方法具有一般性,能用来解决其它该类型的屏障期权的定价问题。     

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturitiesThis shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over timeIn this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issueTo make the problem clearly,we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes(1973), Briys and de Varenne(1997), i.e, the default barrier is KD(t, T) and the recovery rate is(1- ω), where D(t, T) is the price of zero coupon default free bond and ω is a constant(0 ω≤ 1)By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probabilityFurther, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt ≤ KD(t, T)and at the same time, the bondholder will receive(1- ω)Vt KBy introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probabilityNumerical results are presented to show the impact of different parameters to credit spread of bond.     

分形介质中的反常扩散

本文利用适当的标度变换将欧氏空间中的经典扩散方程抗议为分形点阵上的标准扩散方程，并应用该标准扩散方程证明了分形布朗粒子的运动服从反常扩散，同时还讨论了一般分形扩散方程及其渐进解。     

受限分散体系中粒子扩散特性的研究

当微小粒子被限制在两个距离很近的平行平面之间时，其扩散将不同于它在无限空间中的自由扩散. 利用光镊和CCD图像相关处理系统，直接测量了直径1μm的聚苯乙烯小球在不同高度，一定时间间隔内，沿着平行玻片表面方向上布朗运动的距离，并由此得到了样品池上下两个平行表面对分散体系分散相小球扩散特性的影响. 还利用小球偏离物镜焦平面不同距离时的成像状况，用相关运算法确定了小球在纵向上的位置，实现了小球扩散特性与小球在样品池中的纵向位置的关系的研究.     

功率谱密度法标定光镊的三维光阱刚度

采用四象限探测器和功率谱密度法,搭建了一套快速标定光镊三维光阱刚度的测量系统.实验中,用四象限探测器记录微粒做受限布朗运动时的位置信息,用功率谱密度法标定光阱刚度,测得了直径0.97μm SiO2小球和直径1μm PMMA小球的光阱刚度与激光功率的关系.结果表明:对于SiO2小球,当激光功率为50~120mW时,光阱刚度与激光功率成正比;对于PMMA小球,当激光功率为80~130mW时,光阱刚度与激光功率成正比.该光镊系统可用于生物、物理等微观领域研究的高准确度测力系统.     

Total duration of negative surplus for a Brownian motion risk model with interest

In this paper,we consider the Brownian motion risk model with interest.The Laplace transform of the first exit time from the upper barrier before hitting the lower barrier is obtained.Using the obtained result and exploiting the limitation idea,we derive the Laplace transform of total duration of negative surplus.