外币兑换的数学方法：金融工程师方法MATHEMATICAL METHODS FOR FOREIGN EXCHANGE - A FINANCIAL ENGINEER'S APPROACH
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作者： Alexander Lipton 著
出 版 社：
出版时间： 2001-12-1字数：版次： 1页数： 676印刷时间： 2001/10/01开本：印次： 1纸张： 胶版纸I S B N ： 9789810248239包装： 平装内容简介
This comprehensive book presents a systematic and practically oriented approach to mathematical modeling in finance, particularly in the foreign exchange context. It describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic, and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results.
The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.
目录
Preface
I Introduction
1 Foreign exchange markets
1.1 Introduction
1.2 Historical background
1.3 Forex as an asset class
1.4 Spot forex
1.5 Derivatives: forwards, futures, calls, puts, and all that
1.6 References and further reading
II Mathematical preliminaries
2 Elements of probability theory
2.1 Introduction
2.2 Probability spaces
2.3 Random variables
2.4 Convergence of random variables and limit theorems
2.5 References and further reading
3 Discrete-time stochastic engines
3.1 Introduction
3.2 Time series
3.3 Binomial stochastic engines for single- and multi-period markets
3.4 Multinomial stochastic engines
3.5 References and further reading
4 Continuous-time stochastic engines
4.1 Introduction
4.2 Stochastic processes
4.3 Markov processes
4.4 Diffusions
4.5 Wiener processes
4.6 Poisson processes
4.7 SDE and Mappings
4.8 Linear SDEs
4.9 SDEs for jump-diffusions
4.10 Analytical solution of PDEs
4.10.1 Introduction
4.10.2 The reduction method
4.10.3 The Laplace transform method
4.10.4 The eigenfunction expansion method
4.11 Numerical solution of PDEs
4.11.1 Introduction
4.11.2 Explicit, implicit, and Crank-Nicolson schemes for solving one-dimensional problems
4.11.3 ADI scheme for solving two-dimensional problems
4.12 Numerical solution of SDEs
4.12.1 Introduction
4.12.2 Formulation of the problem
4.12.3 The Euler-Maruyama scheme
4.12.4 The Milstein scheme
4.13 References and further reading
III Discrete-time models
5 Single-period markets
5.1 Introduction
5.2 Binomial markets with nonrisky investments
5.3 Binomial markets without nonrisky investments
5.4 General single-period markets
5.5 Economic constraints
5.6 Pricing of contingent claims
5.7 Elementary portfolio theory
……
IV Continuous-time models
Bibliography
Index
