非线性Black-Scholes模型下几何平均亚式期权定价

在非线性Black-Scholes模型下,本文研究了几何平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了几何平均亚式期权的近似定价公式.最后利用Green函数分析了近似结论的误差估计.     

非线性Black-Scholes模型下Bala期权定价

在非线性Black-Scholes模型下,研究了Bala期权定价问题.首先利用双参数摄动方法,将Bala期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了Bala期权的近似定价公式.最后利用Green函数分析了近似结论的误差估计.     

非线性Black-Scholes模型下阶梯期权定价

在非线性Black-Scholes模型下,研究了阶梯期权定价问题.首先利用多尺度方法,将阶梯期权适合的偏微分方程分解成一系列常系数抛物方程;其次通过计算这些常系数抛物型方程的解,给出了修正障碍期权的近似定价公式;最后利用Feymann-Kac公式分析了近似结论的误差估计.     

跳跃扩散型离散算术平均亚式期权的近似价格公式

在标的资产价格遵循跳跃扩散过程条件下 ,研究没有封闭形式解的离散算术平均亚式期权 ,运用二阶 Edgeworth逼近得到离散算术平均亚式期权的近似价格公式 .     

具有浮动执行价的远期生效幂亚式期权定价（英文）

本文研究具有浮动执行价的远期生效幂亚式期权的定价问题.利用鞅方法,首先推导出浮动执行价的远期生效幂亚式几何平均看涨期权价格的显示公式.随后,利用方差减少技术,以此幂亚式几何看涨期权价格公式作为控制变量建立浮动执行价的远期生效幂亚式算术平均看涨期权价格计算的蒙特卡罗模拟算法,获得浮动执行价的远期生效幂亚式期权的定价结果.最后,应用数值实例,分析模型主要参数,时间窗框和幂因子等因素异动时对该类期权价格的影响.计算结果,带控制变量的模拟方法能有效地解决幂亚式期权的定价,以及幂因子对期权价格的影响有显著性作用.     

MC方差减小技术在算术平均亚式外汇期权定价中的应用

建立了利率和汇率波动率均为随机情形下算术平均亚式外汇期权的定价模型.由于其定价问题求解十分困难,运用蒙特卡罗(Monte Carlo)方法并结合控制变量方差减小技术进行模拟,有效地减小了模拟方差,得到了期权定价问题的数值结果.     

Vasiek利率模型下的亚式期权的定价问题和数值分析

本文研究了随机利率满足Vasiccek模型时带有浮动的敲定价格的欧式看涨亚式期权的定价问题.通过对所涉及的退化的抛物型方程的Cauchy问题进行变量代换,我们把状态空间的维数降低了一维.为克服其中的奇异性问题,本文对方程进行了分解,第一部分的方程虽然保持奇性,但是其解具有一个精确表达式;而残差部分满足系数和初始条件都充分光滑的Cauchy问题,我们运用一般的差分方法对该部分进行了有效的数值计算.     

Vasiek利率模型下的亚式期权的定价问题和数值分析

本文研究了随机利率满足Vasiek模型时带有浮动的敲定价格的欧式看涨亚式期权的定价问题.通过对所涉及的退化的抛物型方程的Cauchy问题进行变量代换,我们把状态空间的维数降低了一维.为克服其中的奇异性问题,本文对方程进行了分解,第一部分的方程虽然保持奇性,但是其解具有一个精确表达式;而残差部分满足系数和初始条件都充分光滑的Cauchy问题,我们运用一般的差分方法对该部分进行了有效的数值计算。     

跳扩散模型中亚式期权的定价

本文研究一类跳扩散模型中亚式期权的定价问题，得到了关于算术平均亚式期权的一个简单而统一的算法，并用偏微分方程的技巧将其定价问题归结为一个与路径依赖量无关的一维积分-微分方程的求解问题．     

多尺度高维亚式期权定价的奇摄动解

讨论了一类含有快慢变换尺度的高维亚式期权定价随机波动率模型.根据Girsanov定理和Radon-Nikodym导数实现了期望回报率与无风险利率之间的转化;定义路径依赖型的新算术平均算法,借助Feynman-Kac公式,得到了风险资产期权价格所满足的相应的Black-Scholes方程,运用奇摄动渐近展开方法,得到了期权定价方程的渐近解,并得到其一致有效估计.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by