2009-2010 Bulletin – PDF - SEAS Bulletin - Columbia University

160
OPERATIONS RESEARCH: FIRST AND SECOND YEARS
SEMESTER I SEMESTER II SEMESTER III SEMESTER IV
MATHEMATICS
MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3) 1
PHYSICS
(three tracks, choose one)
Chemistry or physics lab:
C1401 (3) C1402 (3) PHYS C1493 (3) or
C1601 (3.5) C1602 (3.5) PHYS W3081 (2) or
C2801 (4.5) C2802 (4.5) CHEM C1500 (3) or
CHEM C2507 (3) or
CHEM C3085 (4) or
CHEMISTRY
(choose one course)
ENGLISH
COMPOSITION
(three tracks, choose one)
C1403 (3) or C1404 (3) or
C1604 (3.5) or C3045 (3.5)
C1010 (3)
Z1003 (0) C1010 (3)
Z0006 (0) Z1003 (0) C1010 (3)
REQUIRED
NONTECHNICAL
ELECTIVES
ECON W1105 (4) and W1155 recitation (0)
either semester
HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102,
or Global Core (3–4) or Global Core (3–4)
HUMA W1121 or W1123 (3)
either semester
FIRST- AND SECOND-
YEAR DEPT.
REQUIREMENTS
COMPUTER
SCIENCE
PHYSICAL
EDUCATION
GATEWAY LAB
Professional-level course (3) (see pages 12–13) ENGI E2261 (3) SIEO W3600 (4)
C1001 (1) C1002 (1)
E1102 (4) either semester
COMS W1004 (Java) (3) or
COMS W1007 (Java) (3) 2
and
COMS W3134 (3) or
COMS W3137 (4) 2
1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.
IEOR E4620x Pricing models for financial
engineering
Lect: 2.5. 3 pts. Professor Tatevossian.
Prerequisite: IEOR E4700. Models for pricing and
hedging equity, fixed-income, credit-derivative
securities, standard tools for hedging and risk
management, models and theoretical foundations
for pricing equity options (standard European,
American equity options, Asian options), standard
Black-Scholes model (with multi-asset extension),
asset allocation, portfolio optimization, investments
over long-time horizons, and pricing of
fixed-income derivatives (Ho-Lee, Black-Derman-
Toy, Heath-Jarrow-Morton interest-rate model).
Note: Students may not take both IEOR E4630
and DRAN B8835.
IEOR E4630 Asset allocation
Lect: 2.5. 3 pts. Professor Iyengar.
Introduction to modern asset allocation techniques.
The following topics are covered: bond
portfolio selection, mean-variance portfolio selection,
active portfolio selection, robust portfolio
selection, beyond mean-variance: VaR, CVaR
and approximation, and implementation details:
parameter estimation, Bayesian approaches,
transaction and trading costs.
IEOR E4700x and y Introduction to financial
engineering
Lect: 3. 3 pts. Professors Yao and Gallego.
Prerequisite: IEOR E3106 or IEOR E4106, or the
equivalent. Introduction to investment and financial
instruments via portfolio theory and derivative
securities, using basic operations research/engineering
methodology. Portfolio theory, arbitrage;
Markowitz model, market equilibrium, and the
capital asset pricing model. General models for
asset price fluctuations in discrete and continuous
time. Elementary introduction to Brownian motion
and geometric Brownian motion. Option theory;
Black-Scholes equation and call option formula.
Computational methods such as Monte Carlo
simulation.
IEOR E4701s Stochastic models for financial
engineering
Lect: 3. 3 pts. Professor Cont.
Prerequisite: SIEO W4105 or the equivalent.
Review of elements of probability theory, Poisson
processes, exponential distribution, renewal theory.
Wald’s equation. Introduction to discrete-time
Markov chains and applications to queueing theory,
inventory models, branching processes.
SEAS 2009–2010