## Mathematical Finance

*Director: *Jin Ma, Ph.D. *(Mathematics)*

*Codirector: *Michael Magill, Ph.D. *(Economics)*

*Staff Contact: *Nicole Carr

#### Minor in Mathematical Finance

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This interdisciplinary minor was created for students in business, economics and mathematics, whose majors already require some of the introductory course work. Students in other programs are welcome but should expect the minor to require more units than it does for students in those programs.

As with all minors, students must include at least four upper-division courses and four courses dedicated exclusively to this minor (which may be the same four courses). Finally, students must select four courses outside their major department. Economics majors must choose four courses outside of economics; math majors must choose four courses outside of math; business majors must choose four courses outside of the Marshall School of Business. These may be the same courses used to meet the first two conditions.

requirements | units | |
---|---|---|

ECON 203 | Principles of Microeconomics, and | 4 |

ECON 205 | Principles of Macroeconomics, or | 4 |

ECON 351x | Microeconomics for Business, and | 4 |

ECON 352 | Macroeconomics for Business | 4 |

Choose one of the following two sequences (8 units): | ||

ECON 303* | Intermediate Microeconomic Theory | 4 |

ECON 305* | Intermediate Macroeconomic Theory, or | 4 |

BUAD 350* | Macroeconomic Analysis for Business Decisions | 4 |

BUAD 351* | Economic Analysis for Business Decisions | 4 |

Choose two courses, one from each of the following pairs (8 units): | ||

MATH 118x | Fundamental Principles of the Calculus, or | |

MATH 125 | Calculus I | 4 |

MATH 218* | Probability for Business, or | |

MATH 407* | Probability Theory | 4 |

Choose two courses from the following list (8 units): | ||

MATH 126 or MATH 127; MATH 225 or MATH 245; MATH 226 or MATH 227; MATH 408 or MATH 467 |

Choose one course from the following list (4 units): | ||

BUAD 306, BUAD 310, ECON 350*, ECON 357*, FBE 441* |

Choose one course from the following list (4 units): | ||

ECON 452*, ECON 457*, FBE 324*, FBE 421*, FBE 443*, FBE 445*, FBE 459*, FBE 462*, FBE 464* |

Choose one course from the following: | ||

ITP 109x, ITP 110x, CSCI 101 |

Total requirements, for students with no prior course work: 42-43 units |

Students majoring in business administration, economics or mathematics can meet many of these requirements with course work that also satisfies their majors. In addition to those classes, students in those majors must complete the following requirements:

- Business majors satisfy 24 units with course work that is also required for the major and need to complete only 18 units in MATH, ECON and ITP or CSCI
- Economics majors satisfy 20-24 units with course work required for the major (including one major elective), needing only 18-22 units in BUAD, FBE, ITP or CSCI and MATH
- Mathematics majors satisfy 16 units with course work required for the major, needing only 26 units in BUAD, ECON, FBE and ITP or CSCI

#### Progressive Degree Programs in Mathematics

See Mathematics for progressive degree requirements.

#### Master of Science in Mathematical Finance

The objective of this master of science program is to produce graduates with a rigorous foundation in the economic theory and mathematical modeling of financial markets. The program creates an integrated curriculum spanning four disciplines: economics, mathematics, econometrics/statistics and computational/numerical analysis. The program is designed for recent graduates in the fields of applied mathematics, physics and engineering — or for graduates in economics, business and finance with strong mathematical backgrounds — who wish to pursue high-tech finance careers in financial institutions, industry or government.

##### Admission Requirements

Refer to the Requirements for Graduation and the Graduate School for general regulations.

All applicants must take the GRE General Test. Complete transcripts of undergraduate and any graduate level courses are required, as well as a statement of purpose and three recommendation letters. A substantial undergraduate background in mathematics is required, which should include one semester of real analysis or advanced calculus, one semester of linear algebra and one semester of advanced probability/statistics. Candidates with weaker backgrounds may be required to take mathematics classes prior to admission to the program. An undergraduate knowledge of microeconomics and of macroeconomics, and partial differential equations is helpful, although it is not required for admission. Some experience in Matlab and C/C++ programming is also useful.

##### Foreign Language Requirement

There is no foreign language requirement.

##### Course Requirements

Thirty units of course work are required, six core courses and four to five elective courses. Students are required to satisfy a summative experience for degree completion. This will be in the form of registration in 1 unit of MATH 590 Directed Research with a summative report at the end of the term. Topics of research will be determined by the program director. The program consists of:

Required Core Courses (6 courses, 18 units) | Units | |
---|---|---|

Mathematics and Mathematical Finance: | ||

MATH 530ab | Stochastic Calculus and Mathematical Finance | 3-3 |

MATH 512 | Financial Informatics and Simulation (Computer Labs and Practitioner Seminar) | 3 |

MATH 590 | Directed Research | 1 |

Financial Economics and Econometrics: | ||

ECON 613 | Economic and Financial Time Series | 4 |

ECON 659 | Economics of Financial Markets I | 4 |

Elective Courses (4 courses, 12 units) | Units | |
---|---|---|

Computational and Empirical Finance (must take at least 2 courses)*: | ||

FBE 535 | Applied Finance in Fixed Income Securities | 3 |

FBE 554 | Trading and Exchanges | 3 |

FBE 555 | Investment Analysis and Portfolio Management | 3 |

FBE 559 | Management of Financial Risk | 3 |

FBE 589 | Mortgages and Mortgage-Backed Securities and Markets | 3 |

(FBE 555 highly recommended) |

Statistics*: | ||

MATH 541ab | Introduction to Mathematical Statistics | 3-3 |

MATH 543L | Nonparametric Statistics | 3 |

MATH 547 | Methods of Statistical Inference | 3 |

Numerical/Optimization/Other Methods*: | ||

MATH 501 | Numerical Analysis and Computation | 3 |

MATH 502ab | Numerical Analysis | 3-3 |

MATH 504ab | Numerical Solution of Ordinary and Partial Differential Equations | 3-3 |

MATH 505ab | Applied Probability | 3-3 |

MATH 508 | Filtering Theory | 3 |

MATH 509 | Stochastic Differential Equations | 3 |

MATH 585 | Mathematical Theory of Optimal Control | 3 |

Computational and Financial Economics: | ||

ECON 614 | Economic and Financial Time Series II | 4 |

ECON 652 | Economics of Financial Markets II | 4 |

PM 511ab | Data Analysis | 4-4 |

Prerequisites for any of the above courses can be waived based on students’ knowledge of the subject area. Approval from the program director is required.