非線性泛函分析及其應(yīng)用·第4卷：在數(shù)學(xué)物理中的應(yīng)用

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 Probabihty spaces
　　2.4 Convergence of random variables and limit theorems
　　2.5 References and further reading
　3 Discrete-time stochastic engines
　　3.1 Introduction
　　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
　　4.5 Wiener processes
　　4.6 Poisson processes
　　4.7 SDE and Mappings
　　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
　　　4.11.2 Explicit, implicit, and Crank-Nicalson 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 Maruler-Maruyama 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
　　5.6 Pricing of contingent claims
　　5.7 Elementary portfolio theory
　……
Ⅳ Continuous-time models
Bibliography
Index