Financial Markets in Continuous Time连续时间中的金融市场
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作者： Rose-Anne Dana等著
出 版 社： 漓江出版社
出版时间： 2007-9-1字数：版次： 1页数： 326印刷时间： 2007/09/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540711490包装： 平装内容简介
In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.
目录
1The Discrete Case
1.1 A Model with Two Dates and Two States of the World
1.1.1 The Model
1.1.2 Hedging Portfolio, Value of the Option
1.1.3 The Risk-Neutral Measure, Put Call Parity
1.1.4 No Arbitrage Opportunities
1.1.5 The Risk Attached to an Option
1.1.6 Incomplete Markets
1.2 A One-Period Model with (d + 1) Assets and k States of the
World
1.2.1 No Arbitrage Opportunities
1.2.2 Complete Markets
1.2.3 Valuation by Arbitrage in the Case of a Complete Market
1.2.4 Incomplete Markets: the Arbitrage Interval
1.3 Optimal Consumption and Portfolio Choice in a One-Agent Model
1.3.1 The Maximization Problem
1.3.2 An Equilibrium Model with a Representative Agent
1.3.3 The Von Neumann-Morgenstern Model, Risk Aversion
1.3.4 Optimal Choice in the VNM Model
1.3.5 Equilibrium Models with Complete Financial Markets
2Dynamic Models in Discrete Time
2.1 A Model with a Finite Horizon
2.2 Arbitrage with a Finite Horizon
2.2.1 Arbitrage Opportunities
2.2.2 Arbitrage and Martingales
2.3 Trees
2.4 Complete Markets with a Finite Horizon
2.4.1 Characterization
2.5 Valuation
2.5.1 The Complete Market Case
2.6 An Example
2.6.1 The Binomial Model
2.6.2 Option Valuation
2.6.3 Approaching the Black-Scholes Model
2.7 Maximization of the Final Wealth
2.8 Optimal Choice of Consumption and Portfolio
2.9 Infinite Horizon
3 The Black-Scholes Formula
3.1 Stochastic Calculus
3.1.1 Brownian Motion and the Stochastic Integral
3.1.2 It5 Processes. Girsanov's Theorem
3.1.3 It6's Lemma
3.1.4 Multidimensional Processes
3.1.5 Multidimensional ItS's Lemma
3.1.6 Examples
3.2 Arbitrage and Valuation
3.2.1 Financing Strategies
3.2.2 Arbitrage and the Martingale Measure
3.2.3 Valuation
3.3 The Black-Scholes Formula: the One-Dimensional Case
3.3.1 The Model
3.3.2 The Black-Scholes Formula
3.3.3 The Risk-Neutral Measure
3.3.4 Explicit Calculations
3.3.5 Comments on the Black-Scholes Formula
3.4 Extension of the Black-Scholes Formula
3.4.1 Financing Strategies
3.4.2 The State Variable
3.4.3 The Black-Scholes Formula
3.4.4 Special Case
3.4.5 The Risk-Neutral Measure
3.4.6 Example
3.4.7 Applications of the Black-Scholes Formula
4 Portfolios Optimizing Wealth and Consumption
4.1 The Model
4.2 Optimization
4.3 Solution in the Case of Constant Coefficients
4.3.1 Dynamic Programming
4.3.2 The Hamilton-Jacobi Bellman Equation
4.3.3 A Special Case
4.4 Admissible Strategies
……
5 THE Yield curve
6 Equilibrium of Financial markets in discrete time
7 Equilibrium of financial markets in continous time,The complete markets case
8 Incomplete markets
9 Exotic options
A Brownian motion
B Numerical methods
References
Index