Stanford -Master of financial mathematics program
1. STAT 243 Introduction to Mathematical Finance
Lecture notes
(1). Arbitrage Theory in Continuous time, by Tomas Bjork, 3e
(2). Mathematics of Financial Derivatives- A Student Introduction, by Wilmott
2. STAT 240 Statistical Methods in Finance
Text: The Econometrics of Financial Markets,by Campbell John
Reference: Statistical Models and Methods for Financial Markets, by Tze Leung Lai and Haipeng Xing
3. STAT 310 Theory of Probability
(1). lecture notes.。
(2). Real analysis and probability by Dudley,
(3). Probability: theory and examples by Durrett, 4e
(4). Probability and Measure, by Billingsley, 3rd edition,
(5). Probability with martingales, by David Williams,
(6). Brownian Motion and Stochastic Calculus, by Karatzas and Shreve, 推荐
(7). Brownian motion, by Peter Maorters and Yuval Peres, 讲brownian motion有用。
4. MATH 227 Partial Differential Equations and Diffusion Processes
(1) Lecture notes
(2) Partial Differential Equations: An Introduction, by Strauss, 1e
5. MATH 236 Introduction to Stochastic Differential Equations
(1) Stochastic Differential Equations, by Oksendal, 6e
(2) Stochastic Integration And Differential Equations, by Protter, 2e
(3) Probability and random processes, by Grimmett and Stirzaker, 3e
6. MATH 239 Computation and Simulation in Finance
Text: Monte Carlo Methods in Financial Engineering by P. Glasserman
7. MS&E 347 Credit Risk Modeling and Management
(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
8. STAT 220 Stochastic Control in Continuous Time
(1) Lecture notes for master level stochastic processes
(2) STAT 220 lecture notes
(3) Text: Applied Stochastic Control of Jump Diffusions, by Oksendal 1e
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9. STATS 315B Modern Applied Statistics Data Mining
Text: The Elements of Statistical Learning, by Hastie and etc. 2e
10. MS&E 241 Investment Science
Text: Investment Science, by Luenberger,
11. MS&E 321 Stochastic System
1. Lecture notes
2. Adventures in Stochastic Processes, by Resnick
3. A First Course in Stochastic Processes, by Karlin and Taylor,2e
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
12. MS&E 322 Stochastic Calculus and Control
(1) Lecture notes
(2) Text: Stochastic Calculus and Financial Applications, by Steele
13. Asset Pricing theory
(1) Asset Pricing, by Cochrane, revised edition 2e
(2) Asset Pricing Theory by Pennacchi
(3) Dynamic Asset Pricing Theory by Duffie 3e
14. Levy Processes
(1) Financial Modeling with Jump processes,1e
(2) Introductory Lectures on Fluctuations of Levy Processes with Applications by Andreas E. Kyprianou
(3) Levy Processes in Finance Pricing Financial Derivatives by Wim Schoutens
(4) Levy Processes and Stochastic Calculus, 2e by David Applebaum,2e
15. Portfolio optimization
(1) Portfolio Optimization and Performance Analysis by Prigent
(2) Robust Portfolio Optimization and Management by Fabozzi and etc
16. Other general method
(1) Advances in Mathematical Finance by Michael Fu and etc.
(2) Mathematics of Financial Markets 2e by Elliott Kopp
(3) Handbook of Finance Vol 1 Financial Markets and Instruments, Ed. Fabozzi,
(4) Handbook of Operations Research and Managment Sciences, Vol 9, Finance
(5) Handbook of Operations Research and Managment Sciences, Vol 15, Financial Engineering
(6) Interest Rate Models, Theory and Practice, 2e by Damiano Brigo and etc.
(7) Limit Theorems for Stochastic Processes, 2e by Jacod and Shiryaev, (Research 必备书籍)
(8) Martingale Methods in Financial Modelling, 2e by Marek Musiela and Marek Rutkowski
(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.
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