金融数学的书单

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<P>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</P>
<P>大体而言,所需要的知识分为三类<BR>1.数量<BR>2.经济金融<BR>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:<BR>1.Thinking in C++ Vol 1 &amp; 2<BR>2.The C++ Programming Language<BR>另外,还需要data structure &amp; alogrithms的知识 <BR>好在编程高手尽多,这方面也不太需要我业余的意见,呵呵</P>
<P>现在我列一下数量方面的书单<BR>1.概率论</P>
<P>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)</P>
<P>Ross的书适合本科和硕士生,胜在例子详尽<BR>Billingsley的概率论和弱收敛的两本教材是非常好的入门书<BR>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<BR>Durrett的书很流行,不过里面的小错误很多<BR>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<BR>Breiman的书也是经典,概率味比chung的浓<BR>loeve的书可以作为工具书使用</P>
<P>2.随机分析<BR>黄志远的随机分析入门是一本很好的书<BR>严加安的鞅论可以做工具书用<BR>Ross的Inrto to probability model可以做本科生随机过程入门,例子很多<BR>Karlin &amp; Taylor的两本书非常适合硕士生用<BR>resnick的几本书概率味很不错,应用性也很强<BR>oksendal的书是SDE里面最简单的<BR>Karatzas Shreve有好几本书,金融数学的博士不可不读<BR>Revuz Yor的连续鞅是很好的书<BR>Protter的书是严格随机分析里面最容易读的,文笔很好<BR>williams的书深入浅出,入门很合适<BR>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 </P>
<P>3-控制论</P>
<P>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<BR>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)</P>
<P>经典的随机控制书是</P>
<P>1.FLEMING and RISHEL, (1975) Deterministic and Stochastic Optimal Control.<BR>2.KRYLOV, (1980) Controlled diffusion processes<BR>3.BORKAR, (1989) Optimal control of diffusion processes.<BR>4.BENSOUSSAN and LIONS, (1982) Controle Impulsionnel et Inequations Variationnelles</P>
<P>粘性解的标准文献是<BR>1. Crandall, Ishii and Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), <BR>2.Fleming and Soner, Controlled Markov Processes and Viscosity Solutions, 1992. </P>
<P>4.数值算法</P>
<P>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<BR>计算矩阵: Golub and Van Loan, Matrix Computations, 1996<BR>Kushner 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<BR>ROGERS and TALAY, Numerical Methods in Financial Mathematics. 1997.论文集 <BR>Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, 1997. 偏理论,实用性差一点<BR>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</P>
<P>5-时间序列<BR>当然,学习时间序列之前,统计特别是多变量统计要先学好:)</P>
<P>A Guide to Econometrics: by Peter Kennedy可能是最通俗易懂的入门书<BR>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<BR>Box Jerkins的Time Series Analysis: Forecasting &amp; Control,当之无愧的经典<BR>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 <BR>The Econometrics of Financial Markets,by John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay,新经典</P>
<P>现在我们来看一下经济金融方面的书单</P>
<P>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</P>
<P>当然,经济背景也是需要的,比如说<BR>Varian: Microeconomic Analysis(1992)<BR>Samuelson: Economics<BR>如果有时间,最有价值的书大概是Keynes的general principle,<BR>看的时候的感觉会跟第一次学微积分差不多:)</P>
<P>现在我们进入金融书单<BR>1.理论金融</P>
<P>Merton: Continuous time finance<BR>Huang Litzenberger: Foundation for financial economics<BR>Ingersoll: Theorey of financial decision making<BR>Ross: Neoclassical Finance<BR>Ross, Westerfield, Jaffe: Corporate Finance<BR>Duffie: security market<BR>Duffie: Dynamic Asset Pricing Theory<BR>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&amp;A,一般不是很需要数量出身的人,至少到目前为止:)</P>
<P>2.入门和综合类</P>
<P>然后就要开始看一些实际的入门书了<BR>Hull, Options, Futures and Other Derivatives <BR>Baxter and Rennie, Financial Calculus<BR>Shreve:Stochastic Calculus Models for Finance vol 1 &amp; 2<BR>Wilmott: quantitative finance<BR>然后<BR>Bjork: Arbitrage theory in continuous time <BR>Cvitanic, Zapatero: Introduction to the economics and mathematics of financial markets<BR>Elliott, Kopp: Mathematics of Financial markets<BR>Karatzas Shreve: Method of math finance<BR>Musiela and Rutkowski: martingale method for finance<BR>Bielecki, Rutkowski: Credit Risk : Modeling , Valuation and Hedging<BR>Duffie Singleton: Credit Risk<BR>Amman: Credit risk valuation<BR>Taleb:Dynamic Hedging</P>
<P>3. Fixed income<BR>Tuckman: Fixed Income Securities: Tools for Today's Markets是入门的最佳选择</P>
<P>然后,就不得不面对Fabozzi的无数厚书乐:)<BR>Fixed Income Mathematics <BR>Fixed Income Securities <BR>Bond Markets : Analysis and Strategies <BR>The Handbook of Fixed Income Securities,<BR>Handbook of Mortgage Backed Securities <BR>Collateralized Debt Obligations: Structures and Analysis <BR>Interest Rate, Term Structure, and Valuation Modeling </P>
<P>Jessica James, Nick Webber Interest Rate Modelling: Financial Engineering,这本书乱而全<BR>Brigo, Mercurio:Interest Rate Models 数学上难一些<BR>Tavakoli: Collateralized Debt Obligations and Structured Finance <BR>Tavakoli: Credit Derivatives &amp; Synthetic Structures: A Guide to Instruments and Applications<BR>Hayre: Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities </P>
<P>4:其他类<BR>Rebonato有几本很好的书:<BR>Volatility and Correlation : The Perfect Hedger and the Fox <BR>Modern Pricing of Interest-Rate Derivatives : The LIBOR Market Model and Beyond <BR>Interest-Rate Option Models : Understanding, Analysing and Using Models for Exotic Interest-Rate Options </P>
<P>Sch?nbucher:Credit Derivatives Pricing Models: Model, Pricing and Implementation写得很乱但是无可替代<BR>GENCAY: An Introduction to High-Frequency Finance第一本关于high frequency的书<BR>O'Hara:Market Microstructure Theory <BR>Harris:Trading and Exchanges: Market Microstructure for Practitioners </P>

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关键词：金融数学 fixed income Differential econometrics introduction 金融 数学

终于遇到知音了，敢问大哥是何方神圣，遇到同道中人实属不易啊

<P>天那</P>
<P>楼主介绍的那些书, 偶有看过一半, 那是...相-当-的难啊</P>

<P>看过一半也是够厉害了</P>

晕死，读完连博士都可以毕业了！！！

这些书看完一半的可能都不多。。。

很难的，我只看过其中几本，楼主是否全看过了！太牛了！

<P>楼主是为很多想入门的同志做了件大好事．</P>
<P>就像五楼说的，估计读完都可以成博士了，呵呵．</P>

<P>介绍得很详细，多谢楼主了</P>

<P>大哥，这些书有很大一部分没见过也没听说过。how to find them</P>