金融数学的书单

金融数学的书单.直愚Tue, 2005-07-26 00:02 — yijun 金融数学的书单虹桥科教论坛送交者: 直愚 于 July 25, 2005 22:11:46:算起来从95年开始接触这个学科,到现在也有十年了,走了许许多多的弯路,也许,下面的书单,可以让对这个方向有兴趣的人走得比我更快一点....金融数学是一门应用性极强的学科,其特殊之处在于,与许多其他应用学科如生物相比,它的难度更类似于数学物理,而另一方面,它的应用性可以和 engineering相提并论,因为好的结果必须是"有利可图"的,you may cheat a Journal, but you cannot cheat the Market...而更加独特的是,它要求一个人有极其博杂的知识,所以一份好的书单很重要大体而言,所需要的知识分为三类1.数量2.经济金融3.编程,这方面我比较弱,至今还算不上professional programmer:)大致上来说,一个人需要吃透如下LEVEL的书籍:1.Thinking in C++ Vol 1 & 22.The C++ Programming Language另外,还需要data structure & alogrithms的知识好在编程高手尽多,这方面也不太需要我业余的意见,呵呵现在我列一下数量方面的书单1.概率论很不幸的事实是,概率论基本上没有好的中文教材(1998之前,之后我就不清楚了)Ross的书适合本科和硕士生,胜在例子详尽Billingsley的概率论和弱收敛的两本教材是非常好的入门书chung的概率论教材很严格,读起干巴巴的来会有点累,不过是真长工夫的密籍Durrett的书很流行,不过里面的小错误很多如果你真的想理解概率论,feller的两本书是不可不读的,可以说,从高中水平到博士以上学位的读者,都会从中获益---如果要推选概率论里面最有影响的教材,feller的书无可比拟,不过读时要一路自己算,feller书里面错误非常多,虽然都显然是笔误Breiman的书也是经典,概率味比chung的浓loeve的书可以作为工具书使用2.随机分析黄志远的随机分析入门是一本很好的书严加安的鞅论可以做工具书用Ross的Inrto to probability model可以做本科生随机过程入门,例子很多Karlin & Taylor的两本书非常适合硕士生用resnick的几本书概率味很不错,应用性也很强oksendal的书是SDE里面最简单的Karatzas Shreve有好几本书,金融数学的博士不可不读Revuz Yor的连续鞅是很好的书Protter的书是严格随机分析里面最容易读的,文笔很好williams的书深入浅出,入门很合适Chung Williams的书比oksendal稍微难一点,作为应用随机分析的标准教材很不错3-控制论控制论在portfolio selection problem和risk management里面有很多的应用,optimal stopping在美式derivative非常重要金融数学里面用的主要是随机控制,和粘性解(因为operator is often degenerate)经典的随机控制书是1.FLEMING and RISHEL, (1975) Deterministic and Stochastic Optimal Control.2.KRYLOV, (1980) Controlled diffusion processes3.BORKAR, (1989) Optimal control of diffusion processes.4.BENSOUSSAN and LIONS, (1982) Controle Impulsionnel et Inequations Variationnelles粘性解的标准文献是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.数值算法首先,finite difference是极其常用的算法,这方面书籍很多,比如Ames的经典教材计算矩阵: Golub and Van Loan, Matrix Computations, 1996Kushner and Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, 1992. Kushner‘s Markov chain approximation method是控制论里最有用的算法ROGERS and TALAY, Numerical Methods in Financial Mathematics. 1997.论文集Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, 1997. 偏理论,实用性差一点Glasserman, Monte Carlo Methods in Financial Engineering, 2003这本书非常非常实用,可以说是金融数学数值算法的最新经典5-时间序列当然,学习时间序列之前,统计特别是多变量统计要先学好:)A Guide to Econometrics: by Peter Kennedy可能是最通俗易懂的入门书Econometric Analysis,by William H. Greene和Time Series Analysis by James Douglas Hamilton是非常标准的教材,许多学校都在用Box Jerkins的Time Series Analysis: Forecasting & Control,当之无愧的经典Time Series and Dynamic Models by Christian Gourieroux,Gourieroux写了许多书,但似乎他的书不如他的研究文章水准高The Econometrics of Financial Markets,by John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay,新经典现在我们来看一下经济金融方面的书单首先要强调,金融不是经济,经济考虑的是国计民生,环球宇宙之类的大问题,而金融考虑的是money making, risk control之类的充满铜臭味的小问题当然,经济背景也是需要的,比如说Varian: Microeconomic Analysis(1992)Samuelson: Economics如果有时间,最有价值的书大概是Keynes的general principle,看的时候的感觉会跟第一次学微积分差不多:)现在我们进入金融书单1.理论金融Merton: Continuous time financeHuang Litzenberger: Foundation for financial economicsIngersoll: Theorey of financial decision makingRoss: Neoclassical FinanceRoss, Westerfield, Jaffe: Corporate FinanceDuffie: security marketDuffie: Dynamic Asset Pricing Theory当然,金融文献浩如烟海,上面的书单是针对ASSET PRICING一块的,因为这一块最为定量化.至于做underwriting, M&A,一般不是很需要数量出身的人,至少到目前为止:)2.入门和综合类然后就要开始看一些实际的入门书了Hull, Options, Futures and Other DerivativesBaxter and Rennie, Financial CalculusShreve:Stochastic Calculus Models for Finance vol 1 & 2Wilmott: quantitative finance然后Bjork: Arbitrage theory in continuous timeCvitanic, Zapatero: Introduction to the economics and mathematics of financial marketsElliott, Kopp: Mathematics of Financial marketsKaratzas Shreve: Method of math financeMusiela and Rutkowski: martingale method for financeBielecki, Rutkowski: Credit Risk : Modeling , Valuation and HedgingDuffie Singleton: Credit RiskAmman: Credit risk valuationTaleb:Dynamic Hedging3. Fixed incomeTuckman: Fixed Income Securities: Tools for Today‘s Markets是入门的最佳选择然后,就不得不面对Fabozzi的无数厚书乐:)Fixed Income MathematicsFixed Income SecuritiesBond Markets : Analysis and StrategiesThe Handbook of Fixed Income Securities,Handbook of Mortgage Backed SecuritiesCollateralized Debt Obligations: Structures and AnalysisInterest Rate, Term Structure, and Valuation ModelingJessica James, Nick Webber Interest Rate Modelling: Financial Engineering,这本书乱而全Brigo, Mercurio:Interest Rate Models 数学上难一些Tavakoli: Collateralized Debt Obligations and Structured FinanceTavakoli: Credit Derivatives & Synthetic Structures: A Guide to Instruments and ApplicationsHayre: Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities4:其他类Rebonato有几本很好的书:Volatility and Correlation : The Perfect Hedger and the FoxModern Pricing of Interest-Rate Derivatives : The LIBOR Market Model and BeyondInterest-Rate Option Models : Understanding, Analysing and Using Models for Exotic Interest-Rate OptionsSchönbucher:Credit Derivatives Pricing Models: Model, Pricing and Implementation写得很乱但是无可替代GENCAY: An Introduction to High-Frequency Finance第一本关于high frequency的书O‘Hara:Market Microstructure TheoryHarris:Trading and Exchanges: Market Microstructure for Practitioners