算起來從95年開始接觸這個學科,到現在也有十年了,走了許許多多的彎路,也許,下面的書單,可以讓對這個方向有興趣的人走得比我更快一點....

金融數學是一門應用性極強的學科,其特殊之處在於,與許多其他應用學科如生物相比,它的難度更類似於數學物理,而另一方面,它的應用性可以和engineering相提並論,因為好的結果必須是"有利可圖"的,you may cheat a Journal, but you cannot cheat the Market...而更加獨特的是,它要求一個人有極其博雜的知識,所以一份好的書單很重要

大體而言,所需要的知識分為三類

1.數量

2.經濟金融

3.編程,這方面我比較弱,至今還算不上professional programmer:)大致上來說,一個人需要吃透如下LEVEL的書籍:
1.Thinking in C++ Vol 1 & 2
2.The C++ Programming Language
另外,還需要data structure & alogrithms的知識
好在編程高手盡多,這方面也不太需要我業餘的意見,呵呵

現在我列一下數量方面的書單

1.概率論

很不幸的事實是,概率論基本上沒有好的中文教材(1998之前,之後我就不清楚了)

Ross的書適合本科和碩士生,勝在例子詳盡
Billingsley的概率論和弱收斂的兩本教材是非常好的入門書
chung的概率論教材很嚴格,讀起乾巴巴的來會有點累,不過是真長工夫的密籍
Durrett的書很流行,不過裡面的小錯誤很多
如果你真的想理解概率論,feller的兩本書是不可不讀的,可以說,從高中水平到博士以上學位的讀者,都會從中獲益---如果要推選概率論裡面最有影響的教材,feller的書無可比擬,不過讀時要一路自己算,feller書裡面錯誤非常多,雖然都顯然是筆誤
Breiman的書也是經典,概率味比chung的濃
loeve的書可以作為工具書使用

2.隨機分析

黃志遠的隨機分析入門是一本很好的書
嚴加安的鞅論可以做工具書用
Ross的Inrto to probability model可以做本科生隨機過程入門,例子很多
Karlin & Taylor的兩本書非常適合碩士生用
resnick的幾本書概率味很不錯,應用性也很強
oksendal的書是SDE裡面最簡單的
Karatzas Shreve有好幾本書,金融數學的博士不可不讀
Revuz Yor的連續鞅是很好的書
Protter的書是嚴格隨機分析裡面最容易讀的,文筆很好
williams的書深入淺出,入門很合適
Chung Williams的書比oksendal稍微難一點,作為應用隨機分析的標準教材很不錯

3-控制論

控制論在portfolio selection problem和risk management裡面有很多的應用,optimal stopping在美式derivative非常重要
金融數學裡面用的主要是隨機控制,和粘性解(因為operator is often degenerate)

經典的隨機控制書是

1.FLEMING and RISHEL, (1975) Deterministic and Stochastic Optimal Control.
2.KRYLOV, (1980) Controlled diffusion processes
3.BORKAR, (1989) Optimal control of diffusion processes.
4.BENSOUSSAN and LIONS, (1982) Controle Impulsionnel et Inequations Variationnelles

粘性解的標準文獻是
1. Crandall, Ishii and Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992),
2.Fleming and Soner, Controlled Markov Processes and Viscosity Solutions, 1992.

4.數值算法

首先,finite difference是極其常用的算法,這方面書籍很多,比如Ames的經典教材
計算矩陣: Golub and Van Loan, Matrix Computations, 1996
Kushner and Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, 1992. Kushner's Markov chain approximation method是控制論里最有用的算法
ROGERS and TALAY, Numerical Methods in Financial Mathematics. 1997.論文集
Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, 1997. 偏理論,實用性差一點
Glasserman, Monte Carlo Methods in Financial Engineering, 2003這本書非常非常實用,可以說是金融數學數值算法的最新經典

5-時間序列

當然,學習時間序列之前,統計特別是多變量統計要先學好:)

A Guide to Econometrics: by Peter Kennedy可能是最通俗易懂的入門書
Econometric Analysis,by William H. Greene和Time Series Analysis by James Douglas Hamilton是非常標準的教材,許多學校都在用
Box Jerkins的Time Series Analysis: Forecasting & Control,當之無愧的經典
Time Series and Dynamic Models by Christian Gourieroux,Gourieroux寫了許多書,但似乎他的書不如他的研究文章水準高
The Econometrics of Financial Markets,by John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay,新經典

現在我們來看一下經濟金融方面的書單

首先要強調,金融不是經濟,經濟考慮的是國計民生,環球宇宙之類的大問題,而金融考慮的是money making, risk control之類的充滿銅臭味的小問題

當然,經濟背景也是需要的,比如說
Varian: Microeconomic Analysis(1992)
Samuelson: Economics
如果有時間,最有價值的書大概是Keynes的general principle,
看的時候的感覺會跟第一次學微積分差不多:)

現在我們進入金融書單

1.理論金融

Merton: Continuous time finance
Huang Litzenberger: Foundation for financial economics
Ingersoll: Theorey of financial decision making
Ross: Neoclassical Finance
Ross, Westerfield, Jaffe: Corporate Finance
Duffie: security market
Duffie: Dynamic Asset Pricing Theory
當然,金融文獻浩如煙海,上面的書單是針對ASSET PRICING一塊的,因為這一塊最為定量化.至於做underwriting, M&A,一般不是很需要數量出身的人,至少到目前為止:)

2.入門和綜合類

然後就要開始看一些實際的入門書了
Hull, Options, Futures and Other Derivatives
Baxter and Rennie, Financial Calculus
Shreve:Stochastic Calculus Models for Finance vol 1 & 2
Wilmott: quantitative finance

然後
Bjork: Arbitrage theory in continuous time
Cvitanic, Zapatero: Introduction to the economics and mathematics of financial markets
Elliott, Kopp: Mathematics of Financial markets
Karatzas Shreve: Method of math finance
Musiela and Rutkowski: martingale method for finance
Bielecki, Rutkowski: Credit Risk : Modeling , Valuation and Hedging
Duffie Singleton: Credit Risk
Amman: Credit risk valuation
Taleb:Dynamic Hedging

3. Fixed income

Tuckman: Fixed Income Securities: Tools for Today's Markets是入門的最佳選擇

然後,就不得不面對Fabozzi的無數厚書樂:)

Fixed Income Mathematics
Fixed Income Securities
Bond Markets : Analysis and Strategies
The Handbook of Fixed Income Securities,
Handbook of Mortgage Backed Securities
Collateralized Debt Obligations: Structures and Analysis
Interest Rate, Term Structure, and Valuation Modeling

Jessica James, Nick Webber Interest Rate Modelling: Financial Engineering,這本書亂而全
Brigo, Mercurio:Interest Rate Models 數學上難一些
Tavakoli: Collateralized Debt Obligations and Structured Finance
Tavakoli: Credit Derivatives & Synthetic Structures: A Guide to Instruments and Applications
Hayre: Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities

4:其他類

Rebonato有幾本很好的書:

Volatility and Correlation : The Perfect Hedger and the Fox
Modern Pricing of Interest-Rate Derivatives : The LIBOR Market Model and Beyond
Interest-Rate Option Models : Understanding, Analysing and Using Models for Exotic Interest-Rate Options

Schönbucher:Credit Derivatives Pricing Models: Model, Pricing and Implementation寫得很亂但是無可替代
GENCAY: An Introduction to High-Frequency Finance第一本關於high frequency的書
O'Hara:Market Microstructure Theory
Harris:Trading and Exchanges: Market Microstructure for Practitioners