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Master of Science in Financial Mathematics

Admission—To be eligible for admission, students are expected to have excelled in the following courses or their equivalent:

  1. Linear algebra at the level of MATH 104.
  2. Real analysis (Advanced Calculus) at the level of MATH 115.
  3. Basic ordinary and partial differential equations at the level of MATH 131 and 132.
  4. Probability at the level of STATS 116; theory of statistics at the level of STATS 200; and stochastic processes at the level of STATS 217 or, preferably, MATH 136/STATS 219.
  5. Computer programming at the level of CS 106A,B or X.

Some of these courses (e.g. STATS 116) are usually offered during the Summer Quarter so candidates lacking the required background may take them then.

Candidates for admission must take the general Graduate Record Examination and may take the subject test in Mathematics as well. Information about these exams can be found at http://www.gre.org.

Requirements—The program requires completion of 45 units of course work. Ordinarily, four quarters are needed to complete all requirements. Students who do not complete all requirements within three years of admission are terminated from the program.

Of these 45 units, six courses must be taken from the list of required courses and six must be taken from the list of elective courses, available below and on the program web site at http://finmath.stanford.edu/academics/required.html and http://finmath.stanford.edu/academics/electives.html. These courses must be taken for letter grades, but students may elect to take one of the 12 courses CR/NC. An overall grade point average (GPA) of 2.75 is required. There is no thesis requirement.

Any remaining units required to complete the 45 total must be taken from the following options, and may be taken for letter grades or CR/NC:

  1. from the approved list of electives with emphasis on computation, information technology or finance
  2. STATS 200, STATS 217, STATS 218, MATH 131, MATH 132, MATH 202 or ECON 140
  3. additional (practical) CS courses
  4. in the form of an industrial internship in the Bay Area or elsewhere, with the approval and supervision of a faculty member. A written report must be submitted upon completion of the internship. Students who choose to take credit for practical training must sign up for STATS 297 (1-3 units).

Required Courses—In partial fulfillment of the M.S. degree in Financial Mathematics, students must fulfill six required courses, with two from each of the following three core areas:

  1. Stochastic Processes and Statistics
  2. Differential Equations, Modeling, Simulation and Computing
  3. Finance

The selection of these courses is to be done in consultation with the Program Director. The following courses can be counted toward the six required courses:

Mathematics:

MATH 227. Partial Differential Equations and Diffusion Processes

MATH 236. Introduction to Stochastic Differential Equations

MATH 238. Mathematical Finance (same as STATS 250)

MATH 239. Computation and Simulation in Finance

Statistics:

STATS 240. Statistical Methods in Finance

STATS 241. Financial Modeling Methodology and Applications

STATS 242. Algorithmic Trading and Quantitative Strategies

STATS 243. Statistical Methods and Models for Risk Management and Surveillance

STATS 315B. Modern Applied Statistics: Data Mining

STATS 362. Monte Carlo Sampling

Management Science & Engineering:

MS&E 347. Credit Risk: Modeling and Management

Graduate School of Business:

FINANCE 622. Dynamic Asset Pricing Theory

At the Program Director's discretion, courses taken previously that are equivalent to the above may be waived; in which case they must be replaced by elective courses in the same subject area.

Elective Courses—Each candidate must take at least six approved elective courses from the list below, with two from each of the three core areas:

  1. Stochastic Processes and Statistics
  2. Differential Equations, Modeling, Simulation and Computing
  3. Finance

Other elective courses may be authorized by the Program Director if they provide skills relevant to financial mathematics and do not overlap with courses in the candidate's program.

Mathematics:

MATH A136. Stochastic Processes (same as STATS 219)

MATH 180. Introduction to Financial Mathematics

MATH 205A/B. Real Analysis

MATH 220. PDE of Applied Mathematics

MATH 222A. Computational Methods for Fronts, Interfaces, and Waves

MATH 227. Partial Differential Equations and Diffusion Processes

MATH 237. Stochastic Equations and Random Media

MATH 256A/B. Partial Differential Equations

MATH 261A/B. Functional Analysis

MATH 266. Time Frequency Analysis and Wavelets

Statistics:

STATS 202. Data Mining and Analysis

STATS 206. Applied Multivariate Analysis

STATS 207. Introduction to Time Series Analysis

STATS 212. Applied Statistics with SAS

STATS 219. Stochastic Processes (same as MATH 136)

STATS 220. Continuous Time Stochastic Control

STATS 227. Statistical Computing

STATS 235. Decision Making in Financial Services

STATS 237. Time Series Modeling and Forecasting

STATS 240. Statistical Methods in Finance

STATS 243. Introduction to Mathematical Finance (summer version of MATH 180)

STATS 252. Data Mining and Electronic Business

STATS 254. Correspondence Analysis and Related Methods (one time offering Aut 08-09)

STATS 305. Introduction to Statistical Modeling

STATS 306A. Methods for Applied Statistics

STATS 310A/B/C. Theory of Probability

STATS 315A/B/C. Modern Applied Statistics

STATS 317. Stochastic Processes

STATS 318. Modern Markov Chains

STATS 322. Function Estimation in White Noise

STATS 324. Multivariate and Random Matrix Theory

STATS 343. Time Series Analysis

STATS 376A. Information Theory

Computer Science:

CS 106B. Programming Abstractions

CS 106X. Programming Abstractions (Accelerated)

CS 193D. C++

CS 224M. Multi-Agent Systems

CS 295. Software Engineering

CS 229. Machine Learning

CS 249A. Object-Oriented Programming: A Modeling and Simulation Perspective

CS 261. Optimization and Algorithmic Paradigms

CS 339. Topics in Numerical Analysis

CS 365. Randomized Algorithms

Economics:

ECON 190. Introduction to Financial Accounting

ECON 202N-203N. Core Economics: Modules 1 and 2, 5 and 6 - For Non-Economics Ph.D. Students

ECON 210. Core Economics: Modules 3 and 7

ECON 211. Core Economics: Modules 11 and 12

ECON 269. International Financial Markets and Monetary Institutions

ECON 275. Time Series Econometrics

ECON 281. Economics of Uncertainty

ECON 284. Topics in Dynamic Economics

Management Science & Engineering:

MS&E 242H. Investment Science Honors

MS&E 247G. International Financial Management (same as GSB F323)*

MS&G 247S. International Investments

MS&G 272. Entrepreneurial Finance

MS&E 310 . Linear Programming

MS&E 311. Optimization

MS&E 312. Advanced Methods in Numerical Optimization

MS&E 313. Vector Space Optimization

MS&E 323. Simulation Theory

MS&E 339. Approximate Dynamic Programming

MS&E 341. Advanced Economic Analysis

MS&E 342. Advanced Investment Science

MS&E 345. Advanced Topics in Financial Engineering

MS&E 348. Optimization of Uncertainty and Applications in Finance

MS&E 349. Capital Deployment

MS&E 351. Dynamic Programming and Stochastic Control

MS&E 444. Investment Practice

MS&E445. Projects in Wealth Management

Computational & Mathematical Engineering:

CME 340. Computational Methods in Data Mining

Graduate School of Business (GSB), Finance:

FINANCE 320*. Debt Markets

FINANCE 326*. Derivative Securities

FINANCE 328* Portfolio Management

FINANCE 620*. Financial Markets I

FINANCE 621*. Financial Markets II

FINANCE 622*. Dynamic Asset Pricing Theory

FINANCE 629*. Tax and Finance Seminar

Graduate School of Business (GSB), Economic Analysis and Policy:

MGTECON 600. Microeconomic Analysis I*

MGTECON 604. Econometric Methods II*

MGTECON 609. Applied Econometric and Economics Research*

Graduate School of Business (GSB), Operations, Information, and Technology:

OIT 667. Revenue Management*

*Indicates courses of limited enrollment and/or that instructor consent is required for registration.

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