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      • Faculty Publications  (157)

      Mathematical ModelingRemove Mathematical Modeling →

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      • 2008
      • Working Paper

      Firm-Size Distribution and Cross-Country Income Differences

      By: Laura Alfaro, Andrew Charlton and Fabio Kanczuk
      We investigate, using plant-level data for 79 developed and developing countries, whether differences in the allocation of resources across heterogeneous plants are a significant determinant of cross-country differences in income per worker. For this purpose, we use a... View Details
      Keywords: Factories, Labs, and Plants; Developing Countries and Economies; Wages; Resource Allocation; Mathematical Methods
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      Alfaro, Laura, Andrew Charlton, and Fabio Kanczuk. "Firm-Size Distribution and Cross-Country Income Differences." NBER Working Paper Series, No. 14060, June 2008.
      • March 2008 (Revised February 2009)
      • Case

      Transparent Value LLC

      By: Sharon P. Katz, Krishna G. Palepu and Aldo Sesia, Jr.
      Leading index company Dow Jones recently signed a license and joint marketing agreement with Transparent Value LLC, the creator of a new fundamentals-based valuation methodology. The agreement allowed Dow Jones to offer a family of indexes based on the Transparent... View Details
      Keywords: Asset Management; Stocks; Price; Performance Expectations; Mathematical Methods; Valuation
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      Katz, Sharon P., Krishna G. Palepu, and Aldo Sesia, Jr. "Transparent Value LLC." Harvard Business School Case 108-069, March 2008. (Revised February 2009.)
      • 2008
      • Working Paper

      Allocating Marketing Resources

      By: Sunil Gupta and Thomas J. Steenburgh
      Marketing is essential for the organic growth of a company. Not surprisingly, firms spend billions of dollars on marketing. Given these large investments, marketing managers have the responsibility to optimally allocate these resources and demonstrate that these... View Details
      Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods
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      Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." Harvard Business School Working Paper, No. 08-069, February 2008.
      • January 2008
      • Background Note

      Convertible Arbitrage

      By: Joshua Coval and Erik Stafford
      The goal of this simulation is to understand how convertible bonds can be viewed as a portfolio of simpler securities and to introduce an over-the-counter market. The convertible bonds that are available during the simulation are at-the-money and in-the-money so that... View Details
      Keywords: Bonds; Investment Portfolio; Price; Risk Management; Mathematical Methods
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      Coval, Joshua, and Erik Stafford. "Convertible Arbitrage." Harvard Business School Background Note 208-116, January 2008.
      • January 2008 (Revised July 2009)
      • Case

      Forecasting the Great Depression

      By: Walter A. Friedman
      What is proper role of professional economic forecasting in financial decision making? The case presents excerpts from three leading economic forecasters on the eve of, and just after, the stock market crash of October 1929. The first set of excerpts is from Roger... View Details
      Keywords: History; Mathematical Methods; Personal Development and Career; Forecasting and Prediction; Financial Crisis
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      Friedman, Walter A. "Forecasting the Great Depression." Harvard Business School Case 708-046, January 2008. (Revised July 2009.)
      • January 2008
      • Background Note

      Valuing Risky Debt

      By: Joshua Coval and Erik Stafford
      This lesson develops the classical structural approach to pricing and hedging credit risk: Merton's (1974) contingent claims model of debt and equity claims. This model is used to make investment and risk management decisions in an over-the-counter (OTC) market for... View Details
      Keywords: Borrowing and Debt; Credit; Investment; Price; Risk Management; Mathematical Methods; Valuation
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      Coval, Joshua, and Erik Stafford. "Valuing Risky Debt." Harvard Business School Background Note 208-111, January 2008.
      • 2008
      • Chapter

      Matching and Market Design

      By: Muriel Niederle, Alvin E. Roth and Tayfun Sonmez
      Matching is the part of economics concerned with who transacts with whom and how. Models of matching, starting with the Gale-Shapley deferred acceptance algorithm, have been particularly useful in studying labour markets and in helping design clearinghouses to fix... View Details
      Keywords: Market Design; Marketplace Matching; Outcome or Result; Mathematical Methods
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      Niederle, Muriel, Alvin E. Roth, and Tayfun Sonmez. "Matching and Market Design." In The New Palgrave Dictionary of Economics. 2nd ed. Edited by Steven Derlauf and Larry Blume. Hampshire, U.K.: Palgrave Macmillan, 2008.
      • November 2007
      • Background Note

      Asset Allocation I

      By: Joshua D. Coval, Erik Stafford, Rodrigo Osmo, John Jernigan, Zack Page and Paulo Passoni
      The goal of these simulations is to understand the mathematics of mean-variance optimization and the equilibrium pricing of risk if all investors use this rule with common information sets. Simulation A focuses on five to 10 years of monthly sector returns that are... View Details
      Keywords: Asset Pricing; Capital; Investment Return; Risk Management; Mathematical Methods
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      Coval, Joshua D., Erik Stafford, Rodrigo Osmo, John Jernigan, Zack Page, and Paulo Passoni. "Asset Allocation I." Harvard Business School Background Note 208-086, November 2007.
      • November 2007
      • Background Note

      Bayesian Estimation & Black-Litterman

      By: Joshua D. Coval and Erik Stafford
      Describes a practical method for asset allocation that is more robust to estimation errors than the traditional implementation of mean-variance optimization with sample means and covariances. The Bayesian inspired Black-Litterman model is described after introducing... View Details
      Keywords: Asset Management; Investment Portfolio; Mathematical Methods
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      Coval, Joshua D., and Erik Stafford. "Bayesian Estimation & Black-Litterman." Harvard Business School Background Note 208-085, November 2007.
      • October 2007
      • Case

      The AtekPC Project Management Office

      By: F. Warren McFarlan, Mark Keil and John Hupp
      Presents one company's efforts to implement a project management organization, or PMO, and the challenges they faced in doing so. Issues brought out in the case include defining the PMO's purpose and mission, the structure and governance of the PMO, and how to... View Details
      Keywords: Projects; Goals and Objectives; Technological Innovation; Information Technology; Business Strategy; Mathematical Methods; Consulting Industry
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      McFarlan, F. Warren, Mark Keil, and John Hupp. "The AtekPC Project Management Office." Harvard Business School Case 308-049, October 2007.
      • Fourth Quarter 2007
      • Article

      Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk

      By: Dale . F. Gray, Robert C. Merton and Zvi Bodie
      This paper proposes a new approach to measure, analyze, and manage sovereign risk based on the theory and practice of modern contingent claims analysis (CCA). The paper provides a new framework for adapting the CCA model to the sovereign balance sheet in a way that can... View Details
      Keywords: Credit; Investment; Sovereign Finance; Risk Management; Emerging Markets; Market Transactions; Mathematical Methods; Valuation
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      Gray, Dale . F., Robert C. Merton, and Zvi Bodie. "Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk." Special Issue on Credit Analysis. Journal of Investment Management 5, no. 4 (Fourth Quarter 2007): 5–28.
      • September 2007
      • Article

      (Noisy) Communication

      By: Bharat Anand and Ron Shachar
      Communication is central to many settings in marketing and economics. A focal attribute of communication is miscommunication. We model this key characteristic as a noise in the messages communicated, so that the sender of a message is uncertain about its perception by... View Details
      Keywords: Communication Intention and Meaning; Interpersonal Communication; Cost vs Benefits; Marketing Communications; Performance Improvement; Mathematical Methods
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      Anand, Bharat, and Ron Shachar. "(Noisy) Communication." Quantitative Marketing and Economics 5, no. 3 (September 2007): 211–237. (Lead Article.)
      • 2007
      • Working Paper

      Mental Accounting and Small Windfalls: Evidence from an Online Grocer

      By: Katherine L. Milkman, John Beshears, Todd Rogers and Max H. Bazerman
      We study the effect of small windfalls on consumer spending decisions by examining the purchasing behavior of a sample of online grocery shoppers over the course of a year. We compare the purchases customers make when redeeming a $10-off coupon they received from their... View Details
      Keywords: Spending; Consumer Behavior; Mathematical Methods; Food and Beverage Industry; Retail Industry
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      Milkman, Katherine L., John Beshears, Todd Rogers, and Max H. Bazerman. "Mental Accounting and Small Windfalls: Evidence from an Online Grocer." Harvard Business School Working Paper, No. 08-024, September 2007. (Revised March 2008.)
      • Article

      Reputation When Threats and Transfers Are Available

      By: Ernesto Dal Bo, Pedro Dal Bo and Rafael Di Tella
      We present a model where a long-run player is allowed to use both money transfers and threats to influence the decisions of a sequence of short-run players. We show that threats might be used credibly (even in arbitrarily short repeated games) by a long-lived player... View Details
      Keywords: Crime and Corruption; Decision Choices and Conditions; Game Theory; Mathematical Methods; Interests; Power and Influence; Reputation
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      Dal Bo, Ernesto, Pedro Dal Bo, and Rafael Di Tella. "Reputation When Threats and Transfers Are Available." Journal of Economics & Management Strategy 16, no. 3 (Fall 2007).
      • 2007
      • Working Paper

      Optimal Reserve Management and Sovereign Debt

      By: Laura Alfaro and Fabio Kanczuk
      Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign's willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming... View Details
      Keywords: Sovereign Finance; Borrowing and Debt; Financial Liquidity; International Finance; Emerging Markets; Mathematical Methods
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      Alfaro, Laura, and Fabio Kanczuk. "Optimal Reserve Management and Sovereign Debt." NBER Working Paper Series, No. 13216, July 2007.
      • February 2007 (Revised January 2008)
      • Supplement

      Multifactor Models (CW)

      By: Malcolm P. Baker
      Keywords: Asset Pricing; Cost of Capital; Forecasting and Prediction; Investment Funds; Investment Return; Mathematical Methods; Performance Evaluation
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      Baker, Malcolm P. "Multifactor Models (CW)." Harvard Business School Spreadsheet Supplement 207-710, February 2007. (Revised January 2008.)
      • July 2006
      • Article

      Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows

      By: Ramon Casadesus-Masanell and Pankaj Ghemawat
      This paper analyzes a dynamic mixed duopoly in which a profit-maximizing competitor interacts with a competitor that prices at zero (or marginal cost), with the cumulation of output affecting their relative positions over time. The modeling effort is motivated by... View Details
      Keywords: Open Source Software; Demand-side Learning; Network Effects; Linux; Mixed Duopoly; Competitive Dynamics; Business Models; Duopoly and Oligopoly; Information Technology; Applications and Software; Business Model; Mathematical Methods; Digital Platforms; Profit; Balance and Stability; Management Analysis, Tools, and Techniques; SWOT Analysis; Competition; Price; Information Technology Industry
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      Casadesus-Masanell, Ramon, and Pankaj Ghemawat. "Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows." Management Science 52, no. 7 (July 2006): 1072–1084.
      • 2006
      • Chapter

      Advanced Regression Models

      By: Raghuram Iyengar and Sunil Gupta
      Keywords: Mathematical Methods
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      Iyengar, Raghuram, and Sunil Gupta. "Advanced Regression Models." In Handbook of Marketing Research, edited by Rajiv Grover. Sage Publications, 2006.
      • February 2006
      • Teaching Note

      Cost-Volume-Profit Models (TN)

      By: David F. Hawkins, V.G. Narayanan, Michele Jurgens and Jacob Cohen
      Keywords: Mathematical Methods
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      Hawkins, David F., V.G. Narayanan, Michele Jurgens, and Jacob Cohen. "Cost-Volume-Profit Models (TN)." Harvard Business School Teaching Note 106-046, February 2006.
      • January 2006
      • Tutorial

      Cost-Volume Profit Models

      By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
      Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
      Keywords: Volume; Cost; Profit; Mathematical Methods
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      "Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
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