Current courses (2019)

  • B6014: Managerial Statistics (MBA core course; Fall semester)

  • B8816: Quantitative Pricing and Revenue Analytics (MBA elective course; offered annually in the Fall semester)

    Pricing and revenue optimization --or revenue management as it is also called-- focuses on how a firm should set and update pricing and product availability decisions across its various selling channels in order to maximize its profitability. A familiar example comes from the airline industry. The adoption of such systems has transformed the transportation and hospitality industries, and is increasingly important in retail, telecommunications, entertainment, financial services, health care and manufacturing. In parallel, pricing and revenue optimization has become a rapidly expanding practice in consulting services, and a growing area of software and IT development. In this course students learn to identify and exploit opportunities for revenue optimization in different business contexts. This includes a review of the main methodologies that are used in each of these areas, and a survey of current practices in different industries. The course is about evenly split between lectures, cases and guest speakers.

``New'' course (Spring-A 2016)

  • Advanced MBA/PhD course on Electronic trading in limit order book markets (Spring-A 2016)

  • B8134: Electronic trading in modern limit order book markets (Mondays 1045am-2pm; Uris 331)

    Most financial markets are becoming electronic, and typically operated as limit order books. This course will provide an overview of electronic trading, with primary focus on short-term limit order book dynamics. We will overview the practical reality of the equities market, study the literature on a select set of topics that play an important role on short-term market dynamics and execution quality, and get the opportunity to interact with a rich set of market data. In the press, many of these topics are lumped up under the term "High-Frequency Trading (HFT)," and I will try, on the margin, to offer a reasonable and nuanced overview of the area from the broker / HFT / traditional buy-side / regulator viewpoints.

    The topics that we will cover:

    algorithmic trading:

    + high-level overview; popular execution strategies; trading technology overview

    + market data inputs to algorithmic strategies: trading volume; volatility; spreads; depth; market impact models

    + review literature on optimal execution: different modeling frameworks; key findings; what happens in practice

    limit order book:

    + overview

    + point process view

    + queueing model of LOB

    + four illustrative problems: a) estimating time until an order fills; b) optimal execution in LOB and market impact modeling; c) order routing in fragmented markets; d) adverse selection


    + trades and quotes (TAQ) data for US equities with millisecond timestamps going back 4-5 years; starting July 27 the timestamps have microsecond timestamps

    + sample of proprietary trade data 2012-2014 (not current)

    + a software development environment that allows to query and analyze that data ("Onetick") and one to design strategies and backtest them against TAQ data (the latter, "Lime's Strategy Studio," requires coding in C++)

    + database of reference data, e.g., 1 min summaries of US equity activity during 2013-15

    Course organization & goals: This course will be an advanced MBA / PhD course. I am aiming for a 50/50 mix inside the class. A significant part of the course will be on modeling and academic research in the above area; this will leverage and expand on a set of lectures I prepared and gave last spring in London. Another part of the course will review practice and give access to data for students to explore. The methodological content will borrow from tools in stochastic modeling and optimal control. The course will offer an overview of a very interesting and dynamic area, focusing on the mathematical modeling of limit order book markets, and, as explained above, also give broad access to rich data to get a closer view of the short-term behavior of these modern markets.

    Slides from CFM Distinguished Lecture Series, Imperial College, London (2015)

Older courses

  • Stochastic Processing Networks. I taught this course in 1999 and covered topics on product form networks, fluid models and their role in stability analysis and control, heavy traffic approximations of single server queues, and Brownian network models.

  • Seminar in Operations Management. I taught this course in 2001 and mostly covered topics in revenue management and the economics of queues, circa 2000.

  • Seminar on Revenue Management. I have taught this course several times, often jointly with Garrett van Ryzin. It reviews basic topics in the area as covered in the book by Talluri and van Ryzin, plus a collection of "current" papers on various topics in that field. The attached syllabus is from 2004, and is a bit dated. A version of this course will be offered by Garrett van Ryzin in the Fall 2009.


The cases below are used in my two MBA courses; the revenue management cases can also be used in MS and PhD classes . Please follow the appropriate link through Columbia CaseWorks if you are interested on a particular case. All of the cases involve a fair amount of data that students use to build models, optimize decisions, test hypotheses, etc. For some of these cases I have supporting files that can be useful in teaching the respective material; please email me directly for the latter.

  • Analyzing the analysts, with P. Glasserman, 2001. (Managerial Statistics)

    This case is used in the context of a discussion on confidence intervals and hypothesis testing.

  • NY Health Club A & B, 2006. (Revenue Management)

    This case reviews topics related to fitting demand functions (linear, exponential, pareto) to willingness-to-pay (WtP) data, fitting a multinomial logit model to WtP data, and finally fitting an MNL model to choice data using maximum likelihood.

  • Markdown Pricing Optimization at Bloomingdale's A&B, with W. Ke and G. van Ryzin, 2006 (Revenue Management)

    This case reviews topics related to the implementation and performance validation of a revenue management pilot program in a retailing setting.

  • Every Day Medical, 2009 (Revenue Management)

    This case reviews the application of demand modeling and revenue optimization to the problem of choosing a bidding strategy for different keywords in the context of Google AdWords.

  • Hannah Montana, 2009 (Revenue Management)

    This case is on demand modeling, price optimization and product differentiation.