分数布朗运动环境中可转换债券的定价

可转换债券是一种持有者可以将其转换成一定数量股票的债券,可转换债券是证券市场的热点之一.假设股票价格服从几何分数布朗运动过程,在无风险利率、股票期望收益率和股票波动率为常数时,利用风险中性测度,得到可转换债券的定价公式.从而推广的可转换债券的定价.     

分数布朗运动与二元市场模型

证明了对于Hurst指数大于二分之一情形的分数布朗运动的Donsker型逼近定理,使用这种逼近,构造了一个弱收敛于Black-Scholes模型的分数模拟的初级市场模型,得到在此模型中存在着套利机会.     

A note on approximation to subfractional brownian motion

Subfractional Brownian motion can be decomposed in distribution as a sum of independent fractional Brownian motion and a centered Gaussian process with absolutely continuouspaths.This paper proves an approximations of subfractional Brownian motion using the decomposition.     

混合分数布朗运动环境下的幂型亚式期权定价

研究了混合分数布朗运动环境下的几何平均亚式期权的定价问题.假设股票价格在分数布朗运动和布朗运动的共同驱动下,利用拟条件期望方法,得到了幂型几何平均亚式期权的定价公式.并将其推广到有红利支付情形下的几何平均亚式期权定价.     

跳扩散分数布朗运动的随机最大值原理*1

目的：对于一类带有泊松跳过程的分数布朗控制系统,研究随机最优控制输入的存在性问题。方法分数布朗运动的伊藤公式和随机微积分理论。结果证明这类系统的随机最大值原理,控制输入是最优控制输入的充分条件。结论这一理论结果可用于金融数学领域的投资最优控制问题中。     

带漂移布朗运动的一个局部时的Laplace变换

在Borodin和Salminen(2002)文献中有关带漂移布朗运动占位时的Laplace变换结果的基础上,运用Li等(2014)计算局部时的方法,推出了带漂移布朗运动在独立指数时间e_q前,及停留在0处的局部时的Laplace变换表达式Ee~(-λl(e_q,0))=lima→0I(λ/a;0,a,e_q)=((2q+μ~2)~(1/2))/(λ+(2q+μ~2)~(1/2))。当μ=0时,本文结果与标准布朗运动的结果吻合。     

Some open problems in granular matter mechanics

Granular matter is a large assemblage of solid particles, which is fundamentally different from any other type of matters, such as solid and liquid. Most models presented for granular matter are phenomenological and are only suitable for solving engineering problems. Many fundamental mechanical problems remain open. By analyzing characteristics of internal state structure, we propose that granular matter is intrinsically multiscale, i.e. microscale of particle size, mesoscale of force chain, and macroscale of the bulk of granular matter. The correlations among difference scales would be crucial. The mesoscale force chain network is determined by both particle properties and macroscopic boundary conditions. The evolution of the force the chain network contributes to macroscopic mechanical properties of granular matter. In addition, we discuss the drawbacks in simplifying contact forces in the current models, and the difficulties in analyzing the interaction of interstitial fluid in wet granular matter. As an appropriate application of granular matter, debris flow can be studied with granular matter mechanics; meanwhile, debris flow brings more challenges which certainly motivate future studies on granular matter.     

分数布朗运动环境中应用鞅方法定价欧式期权

利用分数布朗运动代替标准布朗运动进行欧式期权定价研究,应用鞅方法推导了到期时刻期权支付函数为幂型的欧式期权的定价,得到在分数布朗运动环境下,具有不同借贷利率的幂型欧式看跌期权的定价公式.丰富了已有期权定价结果,使期权定价公式更贴近于实际.     

Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key factor that determines mechanical properties such as stability, elasticity and sound transmission, which are important for civil engineering and industrial processing. Previous studies have focused on investigations of the global structure of external forces (the boundary condition) and on the probability distribution of individual contact forces. So far, however, precise knowledge of the disordered spatial structure of the force network has remained elusive. Here we report that molecular dynamics simulations of realistic granular packings reveal scale invariance of clusters of particles interacting by means of relatively strong forces. Despite visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, thereby determining a universality class. Unexpectedly, the flat ensemble of force configurations (a simple generalization of equilibrium statistical mechanics) belongs to this universality class, whereas some widely studied simplified models do not. This implies that the elasticity of the grains and their geometrical disorder do not affect the universal mechanical properties.     

平动旋转圆盘内颗粒物质分离现象

采用实验和数值模拟方法研究了单层二元混合颗粒在水平振动条件下的颗粒分离现象.结果表明填充密度对二元颗粒分离有着重要影响.随着填充密度的增加,颗粒团会逐步出现反转和颗粒分离现象.这一研究为揭示颗粒物分离的巴两果效应提供了简单的典型模式.     

颗粒物质三维直剪实验的数值模拟

为了获取断层物质的受压剪切特性,用离散元法生成5种非规则颗粒单元来模拟自然条件下断层物质的直剪过程,以实验数据为参数,探讨了不同法向应力、摩擦系数、颗粒形状、试样颗粒组构对断层物质的剪应力的影响。结果表明,剪应力随法向应力、摩擦系数、非规则颗粒含量的增加而增大,不同法向应力、颗粒形状、试样组构下孔隙率的变化反映了剪应力的变化。     

颗粒物质的两个典型效应研究现状的分析

概述了颗粒物质领域中粮仓现象和巴西坚果效应两个典型现象及其解释理论,分析其理论的成功和不足,并给出一些看法。     

布朗马达的定向流

将生物马达蛋白协调定向运动看作是布朗粒子的运动结果．得到了在内外噪声共同驱动下布朗粒子定态几率流的表达式。定态几率流的方向取决于参数a的大小．在一维周期惯性锯齿势函数中,通过解析计算和数值模拟得到．当内噪声强度一定．随着外噪声强度的增加．定态几率流S增大;且当外噪声强度增加到一定程度．定态几率流S达到一个共同的饱和值。     

物质运动与时空变化的相对论分析

时空记录的不同,实质上是由场的作用变化引起的.相对运动越显著,场的作用变化就越强,从而引起的时空结构变化也越大.     

散体颗粒在滚筒内运动特性的实验研究与数值模拟

通过实验方法研究了不同转速下丝状散体颗粒在滚筒内的运动状态,并采用烟丝作为实验材料,测量其在滚筒内的停留时间.实验结果表明:滚筒烘丝机转速越大,颗粒在抄板的提升作用下运动越剧烈,做圆周运动的时间越少,从而导致颗粒在滚筒内的总停留时间越短.在该实验基础上利用"虚拟颗粒团"方法对滚筒内散体颗粒的运动过程进行数值建模,得到的模拟结果与实验数据吻合较好.因此,采用此数学模型模拟不同滚筒倾角条件下丝状颗粒在滚筒内的运动过程,模拟结果显示:滚筒倾角越大,丝状散体颗粒在抄板和滚筒壁面的综合作用下,纵向运动时间越少,颗粒在滚筒内停留时间越短.     

分数布朗运动环境中几何平均亚式期权的定价

假设股票价格受分数布朗运动驱动下,利用拟条件期望的方法,得到了浮动执行价格的几何平均亚式期权定价公式。     

Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets

The brownian motion of mesoscopic particles is ubiquitous and usually random. But in systems with periodic asymmetric barriers to movement, directed or 'rectified' motion can arise and may even modulate some biological processes. In man-made devices, brownian ratchets and variants based on optical or quantum effects have been exploited to induce directed motion, and the dependence of the amplitude of motion on particle size has led to the size-dependent separation of biomolecules. Here we demonstrate that the one-dimensional pores of a macroporous silicon membrane, etched to exhibit a periodic asymmetric variation in pore diameter, can act as massively parallel and multiply stacked brownian ratchets that are potentially suitable for large-scale particle separations. We show that applying a periodic pressure profile with a mean value of zero to a basin separated by such a membrane induces a periodic flow of water and suspended particles through the pores, resulting in a net motion of the particles from one side of the membrane to the other without moving the liquid itself. We find that the experimentally observed pressure dependence of the particle transport, including an inversion of the transport direction, agrees with calculations of the transport properties in the type of ratchet devices used here.