小米4拆电池教程视频:Stanford 的 MFE program 资料总结

Stanford 的 Master of financial mathematics program 应该是众多MFE program 比较好的一个，每年有许多人申请，而且Stanford本校的Ph. D好多也去辅修一个MFM 的学位。

这些资料和书籍是我根据那个program要求的主干课程整理的，有的除了课本和参考书外，还有lecture notes。这些notes一般就是我上课时老师用的。有些课我也没有上过，如果有notes的话就是我发信去问老师要来的，不过是两年前的东西，可能有点儿旧，但基本的方法应该差不多，还是有一定的参考价值的。我就从简单的课程开始逐一介绍，大伙儿如果觉得哪一部分有用，就根据自己的需要下载好了。

1. STAT 243 Introduction to Mathematical Finance
介绍最基本的方法，应该算是最基础的课程了，比较适合入门。除了lecture notes外，还有两本课本
(1) Arbitrage in Continuous time, by Tomas Bjork, 3rd edition
(2) Mathematics of Financial Derivatives- A Student Introduction, by Wilmott
第一本是新版的，第二本是特别经典的一本书，想入门的朋友可以下来看一看。
 STAT_243_Lecture Notes.rar (1.17 MB) , 
Arbitrage_Theory_in_Continuous_Time_3rd_Edition.pdf (2.57 MB) ,  Wilmott_The Mathematics_of_Financial_Derivatives_A_Student_Introduction.pdf (10.34 MB)

2. STAT 240 Statistical Methods in Finance
非常popular的课程，主要几种于Finance统计方法。任课老师自己有一本书，也用在另外一门课 Statistical Methods and Models for Risk Management and Surveillance.
Text: The Econometrics of Financial Markets, by Campbell John
Reference: Statistical Models and Methods for Financial Markets, by Tze Leung Lai and Haipeng Xing
 Syllabus_and_Text_The_Econometrics_of_Financial_Markets(with solution).rar (6.29 MB) ,  Springer_Statistical_Models_and_Methods_for_Financial_Markets.pdf (7.88 MB)

3. STAT 310 Theory of Probability
特别tough的课，但是如果想搞一些financial engineering的research又不得不学。老师的lecture notes 就已经很全面了，但感觉全都是干货，学起来比较吃力，倒是老师列举的一些课本和参考书读起来效果好的多。
(1) lecture notes. 这是一整年概率课的lecture notes，非常全面。
(2) Real analysis and probability by Dudley, 如果想从理论高度提高自身概率水平，不可错过。
(3) Probability: theory and examples by Durrett, 网上有很多第2，3版的下载，附件里是前几个月刚出的第四版。
(4) Probability and Measure, by Billingsley, 3rd edition, 超经典的理论概率入门。
(5) Probability with martingales, by David Williams, 特别好的入门书籍，我当初上课的时候什么都听不懂，就是拿这本书认真学了一些，慢慢的就懂一点儿了。
(6) Brownian Motion and Stochastic Calculus, by Karatzas and Shreve, 大家肯定都知道这书有多经典，板上好像贴了无数次了，我就不贴了，有兴趣的朋友搜一下就有了。
(7) Brownian motion, by Peter Maorters and Yuval Peres, 讲brownian motion有用。
 STAT_310_classnotes.pdf (4.4 MB) , 
dudley_real_analysis_and_probability.pdf (5.71 MB) ,  Probabilit_Durrett_4ed.pdf (1.74 MB) ,  Probability_and_measure_3rd_Edition.rar (4.35 MB) ,  Williams, Probability with martingales.rar (4.16 MB) ,  Brownian_Motion.pdf (2.74 MB) .

4. MATH 227 Partial Differential Equations and Diffusion Processes
这个program对数学要求比较高，一般好学校PhD level的FE research 需要学PDE，尤其是偏numerical方面的，一般比较好的书是strauss的Partial Differential Equations: An Introduction 和Evans的Partial differential equations
附件里是老师上课的lecture notes和strauss的第一版，我找不到第二版的，那位如果有，不妨发上来共享
(1) Lecture notes
(2) Partial Differential Equations: An Introduction, by Strauss, 1st edition (国内有卖)

 MATH_227_Lecture_Notes.rar (1005.76 KB) , 
partial_differential_equations_an_introduction_strauss.rar (5.43 MB)

5. MATH 236 Introduction to Stochastic Differential Equations
不用说，大家都知道这是FE的必修课程，这里用的书就是Oksendal 的stochastic differential equations 6th edition, 国内可以买到。另外protter的书也值得一看，是不多的从semi-martingale讲的书之一，而且也不是很难。另外，如果概率背景不是很强，又不愿意花许多时间去学理论的人可以看一看Grimmett的probability and random processes，内容笔记简单，而且有保持了概率的严格性。

(1) Stochastic Differential Equations, by Oksendal, 6th edition (国内有卖)
(2) Stochastic Integration And Differential Equations, by Protter, 2nd edition (好像国内也有卖)
(3) Probability and random processes, by Grimmett and Stirzaker, 3rd Edition

 Oksendal_B_Stochastic_differential_equations_an_introduction_with_applications__6ed.pdf (10.04 MB) , 
Protter_Stochastic Integration_And_Differential_Equations_2ED.rar (3.06 MB) ,  Grimmett_Stirzaker_Probability_and_random_processes_3rd_Edition.rar (5.7 MB)

6. MATH 239 Computation and Simulation in Finance
这也是核心课程，FE里许多model都没有analytical solution, 需要numerical solution, 如何能高效地得到比较准确的解恨重要。这就数Glasserman的书，一般大部分学校这个topic的课都用这本书。就我个人感觉来说，真的是一本好书，认真读了并多加实践，就能掌握大部分流行的numerical methods.

Text: Monte Carlo Methods in Financial Engineering by P. Glasserman

 MATH_239_Computation_and_Simulation_in_Finance(syllabus_and_Text).rar (12.66 MB)

7. MS&E 347 Credit Risk Modeling and Management
讲risk modeling的，推荐的课本主要有三本，我想认真学完一本应该就很扎实了。
(1) Credit Risk: Pricing, Measurement and Management by D. Duffie and K. Singleton
(2) Credit Risk: Theory and Applications by D. Lando
(3) An Introduction to Credit Risk Modeling by C. Bluhm, L. Overbeck and C. Wagner

 MSE347-syllabus.pdf (43.28 KB) , 
Credit_Risk_Pricing_Measurement_and_Management.pdf (8.54 MB) ,  Credit_Risk_Modeling_Theory_and_Applications.pdf (2.45 MB) ,  An_Introduction_to_Credit_Risk_Modeling.pdf (4.98 MB) .

8. STAT 220 Stochastic Control in Continuous Time
好像很少看见有学校开stochastic control的课，但finance还是特别有用的。附件里有另外一门随机过程的lecture notes，是修STAT 220 的prerequisite，发上来做个参考。另外就是课程的lecture notes和推荐的课本，如果想在这个方面深入的朋友估计可能会用的到。
(1) Lecture notes for master level stochastic processes
(2) STAT 220 lecture notes
(3) Text: Applied Stochastic Control of Jump Diffusions, by Oksendal (第一版，第二版没有找到)

 Background_Stochastic_processes_nnotes.pdf (2.55 MB) ， 
Stat220notes.pdf (765.31 KB) ，  Oksendal_Applied stochastic_control_of_jump_diffusions.pdf (2.04 MB)

9. STATS 315B Modern Applied Statistics Data Mining
介于理论和实际中的数据挖掘课程。用的课本就是经典hastie的statistical learning theory。在附件里附上了课程的网址，有兴趣的朋友可以上去参考一下。

Text: The Elements of Statistical Learning, by Hastie and etc. 2nd edition

 STATS_315B_coursewebaddress_and_Text.rar (7.18 MB)

下面几门是相关课程，不是MFM program要求的核心课程，但是许多想读FE PhD人都修过
10. MS&E 241 Investment Science
最最基本入门课程，许多不太quantitative的学生都修过，的确比较简单。用的课本就是luenberger的“Investment Science”，我觉得特别适合一点儿背景都没有的朋友，能很快入门。

Text: Investment Science, by Luenberger, (国内有卖)

 Oxford_Investment_Science_David_Luenberger.pdf (17.35 MB)

11. MS&E 321 Stochastic System
高于一般功课 PhD level 的随机过程，比较难，适合想从基础applied stochastic processes向上进阶的朋友。附件里有 老师的lecture notes. 我还把老师推荐而且的确比较有用的参考书也发上来了。顺便说一句，Resnick的书的确很好，如果能学来，基本上一般的概率随机背景就都可以了。Karlin and Taylor的两本书特别适合一心一意要去做金融行业工作的人。Feller的两本书太经典了，适合想从理论上提高的朋友。
1. Lecture notes
2. Adventures in Stochastic Processes, by Resnick
3. A First Course in Stochastic Processes, by Karlin and Taylor，2nd edition
4. A Second Course in Stochastic Processes, by Karlin and Taylor
5. An introduction to probability theory by Feller Vol. 1 and Vol. 2
6. Theory and applications of Stochastic Processes, by Schuss
7. Stochastic Processes, by Parzen

 Lecture_Notes.rar (1.89 MB) , 
Resnick_Adventures_in_Stochastic_Processes.pdf (10.98 MB),  Karlin__Taylor_A_first_course_in_stochastic_processes_2ed.rar (4.79 MB) ,  A_Second_Course_in_Stochastic_Processes_Karlin_Taylor.rar (6.69 MB) ,  feller_introduction_to_probability_theory_vol1.rar (4.9 MB) ,  feller_an_introduction_to_probability_theory_and_its_applications_vol2.rar (10.19 MB) ,  Stochastic_Processes_Parzen.pdf (30.44 MB) ,  Theory_and_Applications_of_Stochastic_Processes.pdf (8.84 MB)

12. MS&E 322 Stochastic Calculus and Control
介于应用和理论之间的Stochastic Calculus, 需要先修过MS&E 321. 老师花了不少力气讲control。
(1) Lecture notes
(2) Text: Stochastic Calculus and Financial Applications, by Steele

 Lecture Notes.rar (7.01 MB) , 
Steele_Stochastic_Calculus_and_Financial_Applications.rar (1.3 MB)

其他相关资源。

13. Asset Pricing theory
附件里有三本书，都很经典，其中duffie的书在国内可以买到
(1) Asset Pricing by Cochrane, revised edition
(2) Asset Pricing Theory by Pennacchi
(3) Dynamic Asset Pricing Theory by Duffie

 Asset_Pricing_Cochrane.pdf (3.88 MB) , 
Pennacchi_Asset_Pricing_Theory.rar (5.58 MB) ,  Dynamic_Asset_Pricing_Theory.pdf (19.14 MB)

14. Levy Processes
Financial modeling with levy processes 这些年很热，附件里基本上囊括了所有我能找到的资料，一些经典书籍因为找不到，所以没有。有兴趣的朋友可以下载
(1) Financial Modeling with Jump processes, (这是超经典的书，附件是第一版，第二版目前还没有找到)
(2) Introductory Lectures on Fluctuations of  Levy Processes with Applications by Andreas E. Kyprianou (很好的学习levy processes的书)
(3) Levy Processes in Finance Pricing Financial Derivatives by Wim Schoutens （对各种model的review）
(4) Levy Processes and Stochastic Calculus, 2nd_Ed, by David Applebaum, 第二版比第一版好了很多

 Financial_Modelling_with_Jump_Processes.rar (4.88 MB),  Introductory_Lectures_on_Fluctuations_of_Levy_Processes_with_Applications.pdf (4.34 MB),  Levy_Processes_In_Finance_Pricing_Financial_Derivatives_Wim_Schoutens.pdf (2.16 MB) ,  Levy_Processes_Stochastic_Calculus_2nd_Ed.pdf (2.69 MB)

15. Portfolio optimization
(1) Portfolio Optimization and Performance Analysis by Prigent
(2) Robust Portfolio Optimization and Management by Fabozzi and etc

 Portfolio_Optimization_and_Performance_Analysis.pdf (3.9 MB) , 
Robust_Portfolio_Optimization_and_Management.PDF (6.51 MB)

16. Other general method
这些内容或许只有做FE research的人会有兴趣，一起都发到这里

(1) Advances in Mathematical Finance by Michael Fu and etc.
(2) Mathematics of Financial Markets 2nd Ed by Elliott Kopp
(3) Handbook of Finance Vol 1 Financial Markets and Instruments, Ed. Fabozzi, (只有第一卷，后面两卷找不到)
(4) Handbook of Operations Research and Managment Sciences, Vol 9, Finance (特别全面的参考书)
(5) Handbook of Operations Research and Managment Sciences, Vol 15, Financial Engineering (高级参考书，涵盖了大部分research中比较popular的方法)
(6) Interest Rate Models, Theory and Practice, 2nd ed. by Damiano Brigo and etc. (专门讲interest rate的好书)
(7) Limit Theorems for Stochastic Processes, 2nd ed. by Jacod and Shiryaev (Research必备书籍)
(8) Martingale Methods in Financial Modelling, 2nd ed. by Marek Musiela and Marek Rutkowski (常使用的一本research用书)
(9) Mathematical Methods for Financial Markets, by Monique Jeanblanc,
(10) Optimal Stopping and Free Boundary Problems, by Peskir and Shiryaev
(11) Optimization Methods in Finance, by Gerard Cornuejols and Reha Tutuncu
(12) Quantitative Finance Vol-1_3 2Nd Ed,
(13) Stochastic Optimization Models in Finance, by Ziemba and etc. 

补充几本有关 credit derivative 的书1. Credit Risk: Models, Derivatives, and Management, Niklas Wagner (Editor), Chapman & Hall , 2008.
2. Understanding Credit Derivatives and Related Instruments （Academic Press Advanced Finance）, by Antulio N. Bomfim, Academic Press, 2004 (NYU 的 finance 的 credit derivatives 的课本)
3. Credit Derivatives Pricing Models: Model, Pricing and Implementation, by Philipp J. Schönbucher and P.J. Schonbucher, Wiley, 2003
4. Credit Derivatives Handbook, Volume 1 and Volume 2, 2006 (两本简易的小册子，内容十分直观)