Numerical Methods in Computational Finance: A Partial Differential Equation (Pde/Fdm) Approach
暫譯: 計算金融中的數值方法：偏微分方程（PDE/FDM）方法

Duffy, Daniel J.

Numerical Methods in Computational Finance: A Partial Differential Equation (Pde/Fdm) Approach
  • 出版商: Wiley
  • 出版日期: 2022-03-21
  • 售價: $2,980
  • 貴賓價: 9.5 折 $2,831
  • 語言: 英文
  • 頁數: 544
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1119719674
  • ISBN-13: 9781119719670

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users.

Part A Mathematical Foundation for One-Factor Problems

Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance.

Part B Mathematical Foundation for Two-Factor Problems

Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks.

Part C The Foundations of the Finite Difference Method (FDM)

Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes.

Part D Advanced Finite Difference Schemes for Two-Factor Problems

Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail.

Part E Test Cases in Computational Finance

Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems.

This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering.

More on computational finance and the author's online courses, see www.datasim.nl.

商品描述(中文翻譯)

這本書是對常微分方程和偏微分方程數學基礎的詳細逐步介紹，包括有限差分法的近似及其在計算金融中的應用。書籍的結構使得初學者、新手和專家用戶都能夠閱讀。

A部分 單因子問題的數學基礎

第1到第7章介紹了理解有限差分法及其在計算金融中應用所需的數學和數值分析概念。

B部分 雙因子問題的數學基礎

第8到第13章討論了與兩個空間變數的橢圓和拋物型偏微分方程相關的一些嚴謹數學技術。特別地，我們開發了在用有限差分法進行近似之前，對偏微分方程進行預處理和修改的策略，從而避免臨時和啟發式的技巧。

C部分 有限差分法（FDM）的基礎

第14到第17章介紹了針對拋物型偏微分方程的初邊值問題的有限差分法的數學背景。它概括了構建穩定和準確的有限差分方案所需的所有背景信息。

D部分 雙因子問題的高級有限差分方案

第18到第22章介紹了一些現代有限差分方法，用於近似雙因子偏微分方程的解。這是我們所知的唯一一本詳細討論這些方法的書籍。

E部分 計算金融中的測試案例

第23到第26章關注基於前面章節的應用。我們討論了廣泛的一因子和雙因子問題的有限差分方案。

這本書適合作為入門級介紹，也作為行業量化分析師和金融碩士/MFE學生使用的現代方法的詳細處理。這些主題在數值分析、科學和工程中都有應用。

有關計算金融和作者的在線課程，請參見 www.datasim.nl。

作者簡介

DANIEL DUFFY, PhD, has BA (Mod), MSc and PhD degrees in pure, applied and numerical mathematics (University of Dublin, Trinity College) and he is active in promoting partial differential equations (PDE) and the Finite Difference Method (FDM) for applications in computational finance. He was responsible for the introduction of the Fractional Step (Soviet Splitting) method and the Alternating Direction Explicit (ADE) method in computational finance. He is the originator of the exponential fitting method for convection-dominated PDEs.

作者簡介(中文翻譯)

丹尼爾·達菲（DANIEL DUFFY），博士，擁有都柏林大學三一學院的純數學、應用數學和數值數學的學士（Mod）、碩士和博士學位。他積極推廣偏微分方程（PDE）和有限差分法（FDM）在計算金融中的應用。他負責引入分數步驟（Soviet Splitting）方法和交替方向顯式（ADE）方法於計算金融領域。他是主導對流主導的偏微分方程的指數擬合方法的創始人。

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