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A Modified Binomial Tree Method for Currency Lookback Options

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Acta Mathematica Sinica,English Series 2000年第3期16卷 445-454页

作者： Min Dai institute of mathematics,Fudan University,shanghai {2.,P.R.china institute of mathematics Fudan University Shanghai 200433 P. R. China

The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of *** the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree *** possesses one order of accuracy and its efficiency is demonstrated by numerical *** convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.

关键词： Modified binomial tree method Currency lookback options Convergence

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2.and LI Zhenqi 1, 3 1. institute of mathematics, Fudan University, shanghai 200433,{2. 2. Department of mathematics,Sichuan Union University, Chengdu 610064,{2. 3. Department of mathematics, Nanchang University, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China Department of mathematics Sichuan Union University Chengdu China Department of mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

On the Neighborhood in Stabilizing Period-T Orbits for Chaotic m Degree Polynomial Dynamical System

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 242-247页

作者： Enguo GU Jiong RUAN and Zhenxun HUANG (institute of mathematics, Fudan University, shanghai 200433,{2.) institute of mathematics Fudan University Shanghai 200433 China

In this paper, a problem of stabilizing a period-T orbit in discrete Chaotic m degree polynomial dynamical systems is studied. The aim is to present a new method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control. A theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate *** ways of implementing the obtained theorem in the Henon map are proposed. Thevalidity of this method is shown by numerical simulation.

关键词： neighborhood of period-T orbit controlling chaotic discrete system gain matrix

TOEPLITZ C-ALGEBRA OVER THE L-SHAPED DOMAIN IN C^m

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Chinese Annals of mathematics,Series B 1996年第3期17卷 325-334页

作者： XU SHENGZHI CHEN XIAOMAN YAN SHAOZONG(institute of mathematics, Fudan University, shanghai 200433,{2.) institute of mathematics Fudan University Shanghai 200433 China

The authors investigate the Toeplitz C-algebra over the L-shaped domain in Cn by thegroupoid approach, and successfully parameterise the unit space of the groupoid associated tothe Toeplitz C-algebra.

关键词： L-shaped domain Toeplitz C-algebra Parameterization

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第4期23卷 439-454页

作者： WANG LIBINinstitute of mathematics, Fudan University, shanghai 200433,{2.. institute of mathematics Fudan University Shanghai 200433 China

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.

关键词： Formation of singularity Quasilinear non-strictly hyperbolic system Weak linear degeneracy

Boundary element-free method for elastodynamics

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Science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. shanghai institute of Applied {2. and Mechanics, shanghai University, shanghai 2.0072. china 2. Department of Civil Engineering, shanghai University, shanghai 2.0072. china 1. shanghai institute of Applied {2. and Mechanics Shanghai University 200072 Shanghai China 2. Department of Civil Engineering Shanghai University 200072 Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

TENSOR PRODUCTS OF JACOBSON RADICALS IN NEST ALGEBRAS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 323-330页

作者： DONG ZHE Departinent of mathematics, Zhejiang University, Hangzhou 31002., china. {2., Fudan University, shanghai 200433, china. Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China Fudan Univ Inst Math Shanghai 200433 Peoples R China

This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2. : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i... 详细信息

关键词： Jacobson radical Tensor product Nest algebra

ALMOST GLOBAL EXISTENCE OF DIRICHLETINITIAL-BOUNDARY VALUE PROBLEM FORNONLINEAR ELASTODYNAMIC SYSTEMOUTSIDE A STAR-SHAPED DOMAIN

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Chinese Annals of mathematics,Series B 2004年第4期25卷 433-454页

作者： XINJIE QINTIEHU instituteofmathematics FudanUniversityShanghai200433China Departmentofmathematics FudanUniversityShanghai200433China

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to ... 详细信息

关键词： Nonlinear elastodynamic system Exterior problem Almost global existence

ON SOME CONSTANTS OF QUASICONFORMAL DEFORMATION AND ZYGMUND CLASS

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Chinese Annals of mathematics,Series B 1995年第3期16卷 325-330页

作者： CHEN JIXIU WEI HANBAI(institute of mathematics, Fudan University, shanghai 200433,{2..) FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

A real-valued function f(x)on belongs to Zygmund class if its Zygmund norm It is proved that when f ∈, there exists an extension F(z)of f to H = {Imz > 0} such that It is also proved that if f(0)=f(1)= 0,then

关键词： Quasiconformal deformation Zygmund class Beurling-Ahlfors extension.