請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63445完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛克民(Keh-Ming Shyue) | |
| dc.contributor.author | You-Gang Chen | en |
| dc.contributor.author | 陳幼剛 | zh_TW |
| dc.date.accessioned | 2021-06-16T16:42:12Z | - |
| dc.date.available | 2012-08-28 | |
| dc.date.copyright | 2012-08-28 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-08-27 | |
| dc.identifier.citation | [1] Arshed Ali, Sirajul Haq, Siraj-ul-Islam, “Mesh Free Collocation Method for
Numerical Solution of Initial-Boundary-Value Problems Using Radial Basis Functions,” Faculty of Engineering Sciences GIK Institute of Engineering Sciences and Technology, Topi, Pakistan. [2] A.R. Fonseca, S.A. Viana, E.J. Silva, R.C. Mesquita, “Imposing Boundary Conditions in The Meshless Local Petrov–Galerkin Method,” Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627 Pampulha, Belo Horizonte, MG, Brazil. [3] Basavaraj Kamavalli, Mohammad Asif Iftikhar, “The Tau Method”, SIAM Journal on Numerical Analysis, Vol. 6, No. 3 (Sep., 1969), pp. 480-492. [4] Basavaraj Kamavalli, Mohammad Asif Iftikhar, “2D Poisson’s equation Solver Using FEM,” Department NADA, KTH, Stockholm, Sweden. [5] Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods: Algorithms, Analysis and Applications. [6] Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods: Algorithms, Analysis and Applications. [7] Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods: Algorithms, Analysis and Applications. [8] Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods: Algorithms, Analysis and Applications. [9] Hans Munthe-Kaas, Tor Sorevik, “Multidimensional pseudo-spectral methods on lattice grids” Dept. of Mathematics, University of Bergen, Johannes Brunsgt. 12, Bergen, Norway. 10] Genz, A., “A Lagrange Extrapolation Algorithm for Sequences of Approximations to Multiple Integrals”, SIAM J. Sci. Stat. Comput., 160~172, 1982. [11] Capstick, S., and Keister, B.D., “Multidimensional quadrature algorithms at higher degree and/or dimension”, Journal of Computational Physics, 123, 267~273, 1996. [12] Willi-Hans Steeb, Yorick Hardy, Matrix Calculus and Kronecker Product: A Practical Approach to Linear and Multilinear Algebra, 308~320, 2011. [13] J.S. Hesthaven, “Spectral penalty methods”, Hunan Computing Center, Changsha, China. [14] J.S. Hesthaven, “Spectral penalty methods”, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. [15] Jan Hesthaven, Sigal Gottlieb, David Gottlieb, Spectral Method for Time-dependent Problems, 133~135, 2011. [16] Zhou Zhen-zhong, “A Spectral Method for a Class of Nonlinear Quasi-parabolic Equations”, Hunan Computing Center, Changsha, China. [17] Peter Kunkel, Volker Mehrmann, Differential-Algebraic Equations: Analysis and Numerical Solution, 13~51, 2006. [18] Xiang XINMIN, “Spectral method for solving the svstem of eauations of Schrijdinger-Klein-Gordon field”, Department of Mathematics, Heilongjiang University, Harbin, China. [19] Suqin Chen, Yingwei Wang, Xionghua Wu, “Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems”, Department of Mathematics, Tongji University, Shanghai 200092, China. [20] Andrea Pascucci, PDE and Martingale Methods in Option Pricing, 1~13,219~255, Department of Mathematics University of Bologna, 2006. [21] John C. Hull, Options, Futures, and Other Derivatives, Chap 1, 5.5, 6.2, Oxford University Press, eight edition, 2012. [22] John C. Hull, Options, Futures, and Other Derivatives, Chap 25, Oxford University Press, eight edition, 2012. [23] Wuming Zhu, “A Spectral Element Method to Price Single and Multi-asset European Options”, Florida state University, 2007 [24] Daniel J. Duffy, Finite Difference Methods in Financial Engineering, Chap 25, Oxford University Press, eight edition, 2012. [25] Daniel J. Duffy, “Numerical Analysis of Jump Diffusion Models; A Partial Differential Equation Approach”. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63445 | - |
| dc.description.abstract | 本論文將類頻譜法運用在幾種金融工程中著名的模型並對其適用範圍、收斂
速度、數值計算的穩定性等方面進行探討。此方法相對於傳統作法被證實有其特 殊的優越性，尤其在特殊邊界問題上的運用。 | zh_TW |
| dc.description.abstract | The aim of this thesis is to address some mathematical issues on the application of
pseudo spectral method on several important models in financial engineering, such as scope of application, speed of convergence, numerical stability, etc. This method has been proven superior with respect to the traditional ones especially for problems with special boundary conditions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T16:42:12Z (GMT). No. of bitstreams: 1 ntu-101-R98221034-1.pdf: 2051271 bytes, checksum: 72da36d12009236c0afbba3a2a49844a (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員會審定書 ...........................................................................................................# 誌謝 ...................................................................................................................................1 中文摘要 ............................................................................................................................2
ABSTRACT .......................................................................................................................3 CONTENTS .......................................................................................................................4 LIST OF FIGURES ............................................................................................................6 LIST OF TABLES ..............................................................................................................7 Chapter 1 Introduction ...............................................................................................8 Chapter 2 Fundamentals of spectral regression methods .....................................10 2.1 Background for general spectral method .......................................................10 2.2 Operations in Rayleigh-Ritz Method.............................................................14 2.3 Rayleigh-Ritz Method with Higher Dimension.............................................17 2.4 Solving ordinary differential equations .........................................................20 2.4.1 Linear problems ...................................................................................20 2.4.2 Nonlinear problems ..............................................................................25 2.4.3 Linear system of equations..................................................................27 2.5 Solving time-dependent partial differential equations..................................30 Chapter 3 Application on option pricing ................................................................36 3.1 Black-Scholes equation for single asset .......................................................36 3.1.1 Discrete Rayleigh-Ritz method for one-dimensional Black-Scholes...37 3.1.2 Numerical results ................................................................................38 3.2 Black-Scholes equation for multiple assets ..................................................39 3.2.1 Discrete Rayleigh-Ritz for Black-Scholes PDE of higher dimension ...39 3.2.2 Numerical results ................................................................................41 Chapter 4 Extension of Black-Scholes equation....................................................42 4.1 American option pricing ...............................................................................42 4.1.1 Imposing free-boundary condition on SRM .......................................43 4.1.2 Numerical resultss ...............................................................................44 4.2 Option pricing in Levy’s model ....................................................................45 4.2.1 Numerical method for integral source.................................................46 4.2.2 Numerical results ................................................................................46 Chapter 5 Conclusions .............................................................................................48 REFERENCE ..................................................................................................................49 | |
| dc.language.iso | en | |
| dc.subject | 布雷克-休斯方程 | zh_TW |
| dc.subject | 偏積微分方程 | zh_TW |
| dc.subject | 正交規則 | zh_TW |
| dc.subject | 正交基底函數 | zh_TW |
| dc.subject | 頻譜法 | zh_TW |
| dc.subject | 自由邊界問題 | zh_TW |
| dc.subject | free boundary condition | en |
| dc.subject | orthogonal basis function | en |
| dc.subject | quadrature rule | en |
| dc.subject | Black-Scholes equation | en |
| dc.subject | partial integro-differential equation | en |
| dc.subject | Spectral method | en |
| dc.title | 高精度算法在金融數學模型中的應用 | zh_TW |
| dc.title | On a High Order Numerical Method for Mathematical Models in
Financial Engineering | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良(I-Liang Chern),郭志禹(Chih-Yu Kuo) | |
| dc.subject.keyword | 頻譜法,正交基底函數,正交規則,布雷克-休斯方程,偏積微分方程,自由邊界問題, | zh_TW |
| dc.subject.keyword | Spectral method,orthogonal basis function,quadrature rule,Black-Scholes equation,partial integro-differential equation,free boundary condition, | en |
| dc.relation.page | 51 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-08-27 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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