双指数障碍链式平方期权的定价研究

考虑次序给定的简单链式平方期权在指数障碍下的期权定价问题,利用Girsanov定理和反射原理等方法,给出了双指数障碍链式平方期权的精确定价公式.     

障碍期权推广到几何平均资产情况下的定价公式

平均期权是亚式期权,其到期收益依赖于某个形式的整个期权有效期内或是其一部分时段内标的资产的平均价格.障碍期权指的是期权是否有效或是否执行决定于标的资产价格在期权有效期内是否碰上障碍.本文主要讨论几何平均资产在期权有效期内设有障碍的期权定价公式,并运用反射原理和回望期权的方法来推导出期权的定价公式.     

Esscher变换下扩展的欧式交换期权定价

文章研究Esscher变换下标的资产价格服从几何布朗运动的扩展的几种欧式交换期权(包括广义交换期权,复合交换期权,障碍交换期权,红绿灯期权)定价问题.首先,给出了带漂移布朗运动的反射原理和性质;其次,借助Gerber和Shiu (1994)给出了多维独立平稳增量过程和二维带漂移布朗运动的Esscher变换定义及其性质;最后,应用Esscher变换的相关理论给出了标的资产价格服从几何布朗运动的扩展的多种欧式交换期权定价公式.特别,本文所得到的期权定价公式与以往文献中给出的结果是一致的.     

允许提前违约的信用衍生产品定价模型

本文运用随机过程中的反射原理 ,停时分布以及障碍期权的定价思想扩展了 Merton( 1 975 )提出的信用衍生产品定价模型 ,对允许提前违约且标的资产间具有相关性的信用衍生产品进行定价 ,并给出了该定价模型的解析解     

双重障碍期权定价

提出双重障碍期权定价的离散放法,反复使用反射原理计算触及障碍的轨线数,并拓展:Boyle-Lau方法计算时步数,而从减少传统Cox-Ross-Rubinstein二项式算法的偏差,数值模拟结果验证所提出离散方法的准确和有效性.     

彩虹障碍期权的定价问题

采用偏微分方程方法研究了彩虹障碍期权的定价问题,推导出它满足的偏微分方程,通过求解这个偏微分方程得出了八种彩虹障碍期权的定价公式及四个看涨——看跌平价公式.     

布朗运动的最大值和阶梯期权

在奇异期权定价中经常遇到的具有漂移的布朗运动的最大值问题,我们运用布朗运动的反射原理和G irsanov定理给出了在有限[0,T]区间上的具有漂移的布朗运动的最大值分布及其与终值的联合分布.然后把其应用到阶梯期权,得到了阶梯期权封闭形式的解.     

混合分数布朗运动环境下欧式障碍期权定价

当股票价格遵循混合分数布朗运动时,利用Δ-对冲和混合分数It8公式,建立混合分数布朗运动下欧式障碍期权定价模型,通过换元法将期权定价的偏微分方程转化为热传导方程,求得显示解.在此基础上,得到欧式障碍期权看涨-看跌平价关系式.由此,再根据敲入-敲出障碍期权关系式可推出障碍期权所有类型的定价公式.     

非线性Black-Scholes模型下障碍期权定

研究了原生资产价格遵循非线性Black-Scholes模型时障碍期权的定价问题.首先,根据混合分数布朗运动的Ito公式和金融市场的复制策略,得到了障碍期权适合的抛物初边值问题.其次,利用扰动理论中单参数摄动展开方法,给出了障碍期权的近似定价公式.最后,利用Feyman-Kac公式分析了近似定价公式的误差估计问题,结果表明近似解一致收敛于相应期权价格的精确解.     

指数Levy跳扩散模型下一类新型期权的定价研究

在指数levy跳扩散模型下,通过在确定的两个时间点之间设置一个特定的常数障碍水平,构造出一类两时间点两资产最大或最小值障碍期权.这种新型期权具有两时间点彩虹期权与障碍期权的双重性质,使得该新型期权在未定权益定价方面的应用更为广泛.最后利用鞅方法,给出了该类期权的定价公式.     

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.     

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.     

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.     

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