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  • All HBS Web  (854)
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    • Research  (639)
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Show Results For

  • All HBS Web  (854)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
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  • August 2018
  • Article

Extrapolation and Bubbles

By: Nicholas Barberis, Robin Greenwood, Lawrence Jin and Andrei Shleifer
We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals: an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors... View Details
Keywords: Bubble; Extrapolation; Volume; Price Bubble; Mathematical Methods
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Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer. "Extrapolation and Bubbles." Journal of Financial Economics 129, no. 2 (August 2018): 203–227.
  • 2016
  • Working Paper

Algorithmic Foundations for Business Strategy

By: Mihnea Moldoveanu
I introduce algorithmic and meta-algorithmic models for the study of strategic problem solving, aimed at illuminating the processes and procedures by which strategic managers and firms deal with complex problems. These models allow us to explore the relationship... View Details
Keywords: Mathematical Methods; Business Strategy
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Moldoveanu, Mihnea. "Algorithmic Foundations for Business Strategy." Harvard Business School Working Paper, No. 17-036, October 2016.
  • 1995
  • Book

Introduction to Statistical Decision Theory

By: John W. Pratt, Howard Raiffa and Robert Schlaifer
Keywords: Mathematical Methods; Decision Making; Theory
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Pratt, John W., Howard Raiffa, and Robert Schlaifer. Introduction to Statistical Decision Theory. MIT Press, 1995.
  • January 1990 (Revised February 1990)
  • Case

MSA: The Software Company--Planning the AMAPs Product Line

By: Robert J. Dolan
MSA has commissioned a major market research study to assess demand potential for a computer software system designed for aerospace and defense contractors. Students must evaluate the results of the study (including a conjoint analysis) to assess whether MSA should... View Details
Keywords: Product; Marketing; Mathematical Methods; Software
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Dolan, Robert J. "MSA: The Software Company--Planning the AMAPs Product Line." Harvard Business School Case 590-069, January 1990. (Revised February 1990.)
  • May 1984 (Revised September 1986)
  • Background Note

Basic Quantitative Analysis for Marketing

By: Robert J. Dolan
Shows how to calculate and use the break-even volume in marketing decision making. View Details
Keywords: Marketing Strategy; Mathematical Methods
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Dolan, Robert J. "Basic Quantitative Analysis for Marketing." Harvard Business School Background Note 584-149, May 1984. (Revised September 1986.)
  • Article

The Shapley Value as a von Neumann-Morgenstern Utility

By: A. E. Roth
Keywords: Value; Mathematical Methods
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Roth, A. E. "The Shapley Value as a von Neumann-Morgenstern Utility." Econometrica 45, no. 3 (April 1977): 657–664.
  • Article

Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

By: Joel Goh, Kian Guan Lim, Melvyn Sim and Weina Zhang
We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using... View Details
Keywords: Robust Optimization; Portfolio Management; Value-at-risk; Mathematical Methods; Finance
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Goh, Joel, Kian Guan Lim, Melvyn Sim, and Weina Zhang. "Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns." European Journal of Operational Research 221, no. 2 (September 1, 2012): 397–406.
  • July 1985 (Revised March 1994)
  • Background Note

Exposure and Hedging

By: David E. Bell
Describes the concept of exposure; the dependence of a goal on an uncertain external event. Describes in detail how hedges may be constructed to eliminate exposure, including the algebra of cross-hedging and hedge ratios. The relevance of regression analysis is... View Details
Keywords: Mathematical Methods; Finance
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Bell, David E. "Exposure and Hedging." Harvard Business School Background Note 186-036, July 1985. (Revised March 1994.)
  • 1976
  • Book

Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America

By: Michael A. Wheeler
Keywords: Society; Mathematical Methods; United States
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Wheeler, Michael A. Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America. New York, NY: W. W. Norton & Company, 1976.
  • 1970
  • Dissertation

Analytical Optimal Control Theory as Applied to Stochastic and Non-Stochastic Economics

By: Robert C. Merton
Keywords: Mathematical Methods; Economics
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Merton, Robert C. "Analytical Optimal Control Theory as Applied to Stochastic and Non-Stochastic Economics." Diss., Massachusetts Institute of Technology (MIT), 1970.
  • January 2018
  • Background Note

Math Tools for Strategists

By: Tarun Khanna and Jan W. Rivkin
Great strategists rely heavily on numbers as they go about their work. This note offers an overview of the highbrow and lowbrow quantitative tools that individuals commonly encounter during strategy courses and in actual strategy work. The note focuses especially on... View Details
Keywords: Mathematical Methods; Strategy
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Khanna, Tarun, and Jan W. Rivkin. "Math Tools for Strategists." Harvard Business School Background Note 718-477, January 2018.
  • 1981
  • Chapter

Exploiting Degeneracy in the Simplex Method

By: André Perold
Keywords: Mathematical Methods; System
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Perold, André. "Exploiting Degeneracy in the Simplex Method." In Large Scale Linear Programming, edited by G. B. Dantzig, M. A. H. Dempster, and Markku Kallio. Laxenburg, Austria: International Institute for Applied Systems Analysis (IIASA), 1981.
  • December 1998
  • Background Note

Note on Low-Tech Marketing Math

By: Robert J. Dolan
Describes basic calculations useful in marketing analysis, break-even analysis, and price-volume relationships. View Details
Keywords: Mathematical Methods; Finance
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Dolan, Robert J. "Note on Low-Tech Marketing Math." Harvard Business School Background Note 599-011, December 1998.
  • 1987
  • Chapter

Laboratory Experimentation in Economics, and Its Relation to Economic Theory

By: A. E. Roth
Keywords: Economics; Mathematical Methods
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Roth, A. E. "Laboratory Experimentation in Economics, and Its Relation to Economic Theory." In Scientific Inquiry in Philosophical Perspective, edited by Nicholas Rescher, 147–167. Lanham: University Press of America, Inc., 1987.
  • Article

The Effects of the Change in the NRMP Matching Algorithm

By: A. E. Roth and Elliott Peranson
Keywords: Change; Mathematical Methods
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Roth, A. E., and Elliott Peranson. "The Effects of the Change in the NRMP Matching Algorithm." JAMA, the Journal of the American Medical Association 278, no. 9 (September 3, 1997): 729–732.
  • 2002
  • Chapter

Foundations of Strategic Equilibria

By: John Hillas and Elon Kohlberg
Keywords: Strategy; Mathematical Methods
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Hillas, John, and Elon Kohlberg. "Foundations of Strategic Equilibria." In Handbook of Game Theory, edited by Robert J. Aumann and Sergiu Hart. Elsevier Science, 2002.
  • 1981
  • Chapter

Risk Aversion and Solutions to Nash's Bargaining Problem

By: R. Kihlstrom, A. E. Roth and D. Schmeidler
Keywords: Risk and Uncertainty; Negotiation; Mathematical Methods
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Kihlstrom, R., A. E. Roth, and D. Schmeidler. "Risk Aversion and Solutions to Nash's Bargaining Problem." In Game Theory and Mathematical Economics, edited by O. Moeschlin and D. Pallaschke, 65–71. Amsterdam: North-Holland Publishing Company, 1981.
  • May 2020
  • Article

Inventory Auditing and Replenishment Using Point-of-Sales Data

By: Achal Bassamboo, Antonio Moreno and Ioannis Stamatopoulos
Spoilage, expiration, damage due to employee/customer handling, employee theft, and customer shoplifting usually are not reflected in inventory records. As a result, records often report phantom inventory, i.e., units of good not available for sale. We derive an... View Details
Keywords: Shelf Availability; Inventory Record Inaccuracy; Optimal Replenishment; Retail Analytics; Performance Effectiveness; Analysis; Mathematical Methods
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Bassamboo, Achal, Antonio Moreno, and Ioannis Stamatopoulos. "Inventory Auditing and Replenishment Using Point-of-Sales Data." Production and Operations Management 29, no. 5 (May 2020): 1219–1231.
  • April 1979
  • Article

Statistical Models of Bond Ratings: A Methodological Inquiry

By: Robert S. Kaplan and Gabriel Urwitz
Keywords: Mathematical Methods; Bonds
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Kaplan, Robert S., and Gabriel Urwitz. "Statistical Models of Bond Ratings: A Methodological Inquiry." Journal of Business (April 1979): 231–261.
  • Article

Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness

By: Michael J Kearns, Seth Neel, Aaron Leon Roth and Zhiwei Steven Wu
The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier (like classification rate or false positive rate) across these groups.... View Details
Keywords: Machine Learning; Algorithms; Fairness; Mathematical Methods
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Kearns, Michael J., Seth Neel, Aaron Leon Roth, and Zhiwei Steven Wu. "Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
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