內容介紹
《數理金融初步(英文版.第3版)》基於期權定價全面介紹數理金融學的基本問題，數理推導嚴密，內容深入淺出，適合受過有限數學訓練的專業交易員和高等院校相關專業本科生閱讀。本書清晰簡潔地闡述了套利、black-scholes期權定價公式、效用函式、最優投資組合選擇、資本資產定價模型等知識。第3版在第2版的基礎上新增了布朗運動與幾何布朗運動、隨機序關係、隨機動態規劃等內容，並且擴展了每一章的習題和參考文獻。
作者介紹
Sheldon M．Ross美國南加州大學工業與系統工程系epstein講座教授。他於1968年在史丹福大學獲得統計學博士學位，1976~2004年在加州大學伯克利分校任教。他發表了大量有關機率與統計方面的學術論文，並出版了多部教材。他還創辦了《probability in engineering and informational sciences》雜誌並一直擔任主編。他是數理統計學會會員，榮獲過美國科學家humboldt獎。作品目錄
《數理金融初步(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
