數(shù)理金融初步(英文版·第3版)

內(nèi)容概要

《數(shù)理金融初步(英文版.第3版)》基于期權(quán)定價全面介紹數(shù)理金融學(xué)的基本問題，數(shù)理推導(dǎo)嚴(yán)密，內(nèi)容深入淺出，適合受過有限數(shù)學(xué)訓(xùn)練的專業(yè)交易員和高等院校相關(guān)專業(yè)本科生閱讀。本書清晰簡潔地闡述了套利、black-scholes期權(quán)定價公式、效用函數(shù)、最優(yōu)投資組合選擇、資本資產(chǎn)定價模型等知識。
第3版在第2版的基礎(chǔ)上新增了布朗運(yùn)動與幾何布朗運(yùn)動、隨機(jī)序關(guān)系、隨機(jī)動態(tài)規(guī)劃等內(nèi)容，并且擴(kuò)展了每一章的習(xí)題和參考文獻(xiàn)。

作者簡介

Sheldon M．Ross美國南加州大學(xué)工業(yè)與系統(tǒng)工程系epstein講座教授。他于1968年在斯坦福大學(xué)獲得統(tǒng)計學(xué)博士學(xué)位，1976~2004年在加州大學(xué)伯克利分校任教。他發(fā)表了大量有關(guān)概率與統(tǒng)計方面的學(xué)術(shù)論文，并出版了多部教材。他還創(chuàng)辦了《probability in engineering and informational sciences》雜志并一直擔(dān)任主編。他是數(shù)理統(tǒng)計學(xué)會會員，榮獲過美國科學(xué)家humboldt獎。

書籍目錄

《數(shù)理金融初步(英文版.第3版)》
introduction and preface
1 probability
1.1 probabilities and events
1.2 conditional probability
1.3 random variables and expected values
1.4 covariance and correlation
1.5 conditional expectation
1.6 exercises
2 normal random variables
2.1 continuous random variables
2.2 normal random variables
2.3 properties of normal random variables
2.4 the central limit theorem
2.5 exercises
3 brownian motion and geometric brownian motion
3.1 brownian motion
3.2 brownian motion as a limit of simpler models
3.3 geometric brownian motion
3.3.1 geometric brownian motion as a limit of simpler models
.3.4 *the maximum variable
3.5 the cameron-martin theorem
3.6 exercises
4 interest rates and present value analysis
4.1 interest rates
4.2 present value analysis
4.3 rate of return
4.4 continuously vax)ring interest rates
4.5 exercises
5 pricing contracts via arbitrage
5.1 an example in options pricing
5.2 other examples of pricing via arbitrage
5.3 exercises
6 the arbitrage theorem
6.1 the arbitrage theorem
6.2 the multiperiod binomial model
6.3 proof of the arbitrage theorem
6.4 exercises
7 the black-scholes formula
7.1 introduction
7.2 the black-scholes formula
7.3 properties of the black-scholes option cost
7.4 the delta hedging arbitrage strategy
7.5 some derivations
7.5.1 the black-scholes formula
7.5.2 the partial derivatives
7.6 european put options
7.7 exercises
8 additional results on options
8.1 introduction
8.2 call options on dividend-paying securities
8.2.1 the dividend for each share of the security is paid continuously in time at a rate equal to a fixed fraction f of the price of the security
8.2.2 for each share owned, a single payment of fs(td) is made at time td
8.2.3 for each share owned, a fixed amount d is to be paid at time td
8.3 pricing american put options
8.4 adding jumps to geometric brownian motion
8.4.1 when the jump distribution is lognormal
8.4.2 when the jump distribution is general
8.5 estimating the volatility parameter
8.5.1 estimating a population mean and variance
8.5.2 the standard estimator of volatility
8.5.3 using opening and closing data
8.5.4 using opening, closing, and high-low data
8.6 some comments
8.6.1 when the option cost differs from the black-scholes formula
8.6.2 when the interest rate changes
8.6.3 final comments
8.7 appendix
8.8 exercises
9 valuing by expected utility
9.1 limitations of arbitrage pricing
9.2 valuing investments by expected utility
9.3 the portfolio selection problem
9.3.1 estimating covariances
9.4 value at risk and conditional value at risk
9.5 the capital assets pricing model
9.6 rates of return: single-period and geometric brownian motion
9.7 exercises
10 stochastic order relations
10.1 first-order stochastic dominance
10.2 using coupling to show stochastic dominance
10.3 likelihood ratio ordering
10.4 a single-period investment problem
10.5 second-order dominance
10.5.1 normal random variables
10.5.2 more on second-order dominance
10.6 exercises
11 optimization models
11.1 introduction
11.2 a deterministic optimization model
11.2.1 a general solution technique based on dynamic programming
11.2.2 a solution technique for concave return functions
11.2.3 the knapsack problem
11.3 probabilistic optimization problems
11.3.1 a gambling model with unknown win probabilities
11.3.2 an investment allocation model
11.4 exercises
12 stochastic dynamic programming
12.1 the stochastic dynamic programming problem
12.2 infinite time models
12.3 optimal stopping problems
12.4 exercises
13 exotic options
13.1 introduction
13.2 barrier options
13.3 asian and lookback options
13.4 monte carlo simulation
13.5 pricing exotic options by simulation
13.6 more efficient simulation estimators
13.6.1 control and antithetic variables in the simulation of asian and lookback option valuations
13.6.2 combining conditional expectation and importance sampling in the simulation of barrier option valuations
13.7 options with nonlinear payoffs
13.8 pricing approximations via multiperiod binomial models
13.9 continuous time approximations of barrier and lookback options
13.10 exercises
14 beyond geometric brownian motion models
14.1 introduction
14.2 crude oil data
14.3 models for the crude oil data
14.4 final comments
15 autoregressive models and mean reversion
15.1 the autoregressive model
15.2 valuing options by their expected return
15.3 mean reversion
15.4 exercises
index

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