财政工程的有限差方法电子书籍txtpdf网盘下载网站

内容概要

The world of quantitative finance (QF) is one of the fastest growing areas of research and its prtical applications to derivatives pricing problem* Since the discovery of the famous Blk-Scholes equation in the 1970s we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others* Gone are the days when it was psible to price these derivatives analytically* For mt problems we must resort to some kind of approximate method*

书籍目录

0 Goals of this Book and Global Overview*PART I THE CONTINUOUS THEORY OF PARTIAL DIFFERENTIAL EQUATIONS* 1 An Introduction to Ordinary Differential Equations* 　2 An Introduction to Partial Differential Equations* 　3 Second-Order Parabolic Differential Equations* 　4 An Introduction to the Heat Equation in One Dimension* 　5 An Introduction to the Method of Charteristics* PART II FINITE DIFFERENCE METHODS: THE FUNDAMENTALS* 　6 AnIntroduction to the Finite Difference Method* 　7 An Introduction to the Method of Lines* 　8 General Theory of the Finite Difference Method* 　9 Finite Difference Schemes for First-Order Partial Differential Equations* 　10 FDM for the One-Dimensional Convection–Diffusion Equation* 　11 Exponentially Fitted Finite Difference Schemes* PART III APPLYING FDM TO ONE-FACTOR INSTRUMENT PRICING* 　12 Ext Solutions and Explicit Finite Difference Method for One-Ftor Models* 　13 An Introduction to the Trinomial Method* 　14 Exponentially Fitted Difference Schemes for Barrier Options* 　15 Advanced Issues in Barrier and Lookbk Option Modelling* 　16 The Meshless (Meshfree) Method in Financial Engineering* 　17 Extending the Blk–Scholes Model: Jump Processes* PART IV FDM FOR MULTIDIMENSIONAL PROBLEMS* 　18 Finite Difference Schemes for Multidimensional Problems* 　19 An Introduction to Alternating Direction Implicit and Splitting Methods* 　20 Advanced Operator Splitting Methods: Frtional Steps* 　21 Modern Splitting Methods* PART V APPLYING FDM TO MULTI-FACTOR INSTRUMENT PRICING* 　22 Options with Stochastic Volatility: The Heston Model* 　23 Finite Difference Methods for Asian Options and Other ‘Mixed’ Problems* 　24 Multi-Asset Options* 　25 Finite Difference Methods for Fixed-Ine Problems* PART VI FREE AND MOVING BOUNDARY VALUE PROBLEMS* 　26 Bkground to Free and Moving Boundary Value Problems* 　27 Numerical Methods for Free Boundary Value Problems: Front-Fixing Methods* 　28 Viscity Solutions and Penalty Methods for American Option Problems* 　29 Variational Formulation of American Option Problems* PART VII DESIGN AND IMPLEMENTATION IN C++* 　30 Finding the Appropriate Finite Difference Schemes for your Financial Engineering Problem* 　　31 Design and Implementation of First-Order Problems* 　32 Moving to Blk–Scholes* 　33 C++ Class Hierarchies for One-Ftor and Two-Ftor Payoffs* Appendices* 　A1 An introduction to integral and partial integro-differential equations* 　A2 An introduction to the finite element method* Bibliography* Index*

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