Columbia Business School

Electives: Management Science

Security pricing: models and computation Mathematical methods II
Statistical methods in business and economic research Selected topics in mathematical models
Applied multivariate statistics Foundations of optimization
Negotiations and decision making Inventory planning models
Decision models II Inventory theory
Various seminars in decision and risk analysis Logistics and distribution management
Mathematical methods I

Instructors for courses in decision and risk analysis
S. Browne F. Chen A. Federgruen P. Glasserman
L. Green P. Kolesar D. Lehmann S. Masri

Decision, Risk and Operations department


B8835 Security pricing: models and computation
(terms offered: fall, spring)

Prerequisites: B6014, B6015, Finance B6302 or instructor's permission.

The development of models for security pricing, portfolio analysis and risk management. Particular attention is given to computer-based models for option pricing and hedging; mean-variance analysis; multiperiod portfolio optimization; analysis of the term structure and interest rate­sensitive securities, including swaps, swaptions and mortgage-backed securities. Techniques used include binomial methods, Monte Carlo simulation, linear and quadratic programming and regression. Models are implemented and tested in spreadsheets or specialized software.


B8831 Statistical methods in business and economic research
Prerequisite: B6014 or the equivalent.

Primary emphasis is on the construction of explanatory probabilistic models. Preliminary coverage of some probability theory; moments and cumulants; moment generating functions; major probability distributions and their interrelationships; methods of estimation, including maximum likelihood and the method of moments; and tests of goodness of fit.


B8832 Applied multivariate statistics (term offered: summer)
Prerequisite: B6014.

A comprehensive introductory survey of multivariate methods. Matrix algebra, simple and multiple regression, data reduction, factor analysis, discriminant analysis, multidimensional scaling, experimental design and analysis of variance.


B8833/B8412 Negotiations and decision making
Prerequisite: B6014 or the equivalent.

This course is about the art and science of creating agreements between two or more parties. Students discuss and apply concepts developed in behavioral science and game theory as guides to improved negotiating. Students will develop and sharpen negotiating skills by negotiating with other students in real-world cases. This course offers a refreshing perspective on both competition and cooperation.

Students wishing to enroll in the course should register for Human Resource Management B8412-06, Managerial Negotiations, in the fall or B8412-07 in the spring. These sections are different from the other sections of B8412 in that instructors place greater emphasis on game-theoretical foundations of the negotiation process.


B8834 Decision models II
(term offered: fall)

Prerequisite: B6015 or the equivalent.

The solution of management problems using mathematical modeling. Emphasis is placed on the application of the models through the use of case studies. Topics include advanced optimization models, Markov processes, queuing models, dynamic programming and simulation. Applications are selected from production management, inventory control, finance, corporate strategic planning, facility layout and design and other management areas.


B9801 Various seminars in management science
(term offered: spring)

Special topics in the area of management science. Recent topics have included analytical models in finance, discrete event simulation, distribution models, multi-echelon inventory management, planning models for portfolio management and securities pricing and Brownian and fluid models of manufacturing systems.


B9821 Mathematical methods I
(term offered: fall)

Primarily for PhD candidates; open to qualified MBA candidates with the instructor's permission.
Prerequisite: differential and integral calculus.

The first in a two-course sequence in probability and statistics. Topics include basic probability theory, general characteristics of random variables, particularly probability distributions that are frequently used in statistics, and elementary random (stochastic) processes. The intent is to develop in the student an intuitive feel for the subject of probability theory and enable him or her to think probabilistically.


B9822 Mathematical methods II
(term offered: spring)

Primarily for PhD candidates; open to qualified MBA candidates with the instructor's permission.
Prerequisite: B9821.

A rigorous exposition of the fundamentals of mathematical statistics. In particular, estimation theory and hypothesis testing are covered via the likelihood principle. A thorough introduction to linear models follows, with emphasis on regression and analysis of variance.


B9823 Selected topics in mathematical models
(term offered: summer)

Primarily for PhD candidates; open to qualified MBA candidates with the instructor's permission.
Prerequisites: B9821 and B9822, or B6015 and B8831 or their equivalents and the instructor's permission.

Topics include stochastic models in business research, covering an introduction to and analysis of stochastic models used in allied business fields, such as marketing, management, economics and finance, and advanced statistical modeling and analysis for business research. Emphasis on independent study.


B9824 Foundations of optimization
(term offered: fall)

Mathematical optimization is essential for modeling rational behavior, competition and decision making. It is therefore used extensively as a theoretical tool in a variety of fields, including economics, finance, marketing, engineering, operations management and management science. This course is intended to provide PhD students in these fields with a firm foundation in the theory of mathematical optimization. Both static and dynamic optimization (optimal control) are covered. Topics include unconstrained and constrained nonlinear programming, Lagrange multiplier theory, duality, convex analysis, min-max theorems, the Euler conditions, the Pontryagin maximum principle and vector space optimization methods.

The following three courses, offered jointly by the Business School and the Department of Industrial Engineering and Operations Research of the School of Engineering and Applied Science, carry interdisciplinary 6000-level numbers. However, all three are taught at a level equivalent to Business 8000- and 9000-level courses.


Decision and Risk Analysis--Operations Research
W6406 Inventory planning models
(term offered: fall)

Prerequisite: Operations Research E4601 Linear Programming or B6015 Decision Models.

Characterization and computation of optimal policies for dynamic inventory and production planning models with deterministic requirements.


Decision and Risk Analysis--Operations Research
W6408 Inventory theory

Prerequisite: a one-term, calculus-based graduate probability course.

Construction and analysis of mathematical models used in the design and analysis of inventory systems. Deterministic and stochastic demands and lead times. Optimality of (s, S) policies. Multiproduct and multi-echelon systems. Computational methods.


Decision and Risk Analysis--Operations Research
W6410 Logistics and distribution management
(term offered: spring)

Prerequisites: Operations Research E4500 Dynamic Programming and Operations Research E4601 Linear Programming (or, as an alternative to both of the previous courses, B8834).

Models are studied for problems arising in the planning of the logistics of multi-echelon systems. Focus is on the following operational and strategic problems: facility location; vehicle routing; inventory allocation; and capacity expansion. Emphasis is on devices to integrate these areas. Case studies and applications.