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

Show Results For

  • All HBS Web  (854)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
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  • January 2016
  • Article

Zooming In: A Practical Manual for Identifying Geographic Clusters

By: Juan Alcacer and Minyuan Zhao
This paper takes a close look at the reasons, procedures, and results of cluster identification methods. Despite being a popular research topic in strategy, economics, and sociology, geographic clusters are often studied with little consideration given to the... View Details
Keywords: Mathematical Methods
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Alcacer, Juan, and Minyuan Zhao. "Zooming In: A Practical Manual for Identifying Geographic Clusters." Strategic Management Journal 37, no. 1 (January 2016): 10–21.
  • 2013
  • Chapter

Weighted Generating Functions for Type II Lattices and Codes

By: Noam D. Elkies and Scott Duke Kominers
We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we... View Details
Keywords: Mathematical Methods
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Elkies, Noam D., and Scott Duke Kominers. "Weighted Generating Functions for Type II Lattices and Codes." In Quadratic and Higher Degree Forms. Vol. 31, edited by Alladi Krishnaswami, Manjul Bhargava, David Savitt, and Pham Huu Tiep, 63–108. Developments in Mathematics. Springer, 2013.
  • Article

Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

By: Daniel M. Kane and Scott Duke Kominers
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details
Keywords: Mathematical Methods
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Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
  • 1987
  • Chapter

Continuous-Time Stochastic Models

By: Robert C. Merton
Keywords: Mathematical Methods
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Merton, Robert C. "Continuous-Time Stochastic Models." In The New Palgrave: A Dictionary of Economic Theory and Doctrine, edited by John Eatwell, Murray Milgate, and Peter Newman. London: Macmillan Press, 1987. (Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd., 1992.)
  • February 1996
  • Exercise

Problems in Variance Analysis

By: William J. Bruns Jr.
Keywords: Mathematical Methods
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Bruns, William J., Jr. "Problems in Variance Analysis." Harvard Business School Exercise 196-120, February 1996.
  • May 1983
  • Article

Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming

By: André Perold and R. Meidan
Keywords: Mathematical Methods
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Perold, André, and R. Meidan. "Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming." Journal of Optimization Theory and Applications 40, no. 1 (May 1983): 61–76.
  • February 2005 (Revised November 2006)
  • Background Note

Using Data Desk for Statistical Analysis

By: Frances X. Frei and Dennis Campbell
Describes how to use the Data Desk software package to perform statistical analysis. View Details
Keywords: Mathematical Methods
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Frei, Frances X., and Dennis Campbell. "Using Data Desk for Statistical Analysis." Harvard Business School Background Note 605-060, February 2005. (Revised November 2006.)
  • March 2004
  • Tutorial

Variance Analysis Tutorial

By: David F. Hawkins and Jacob Cohen
An interactive tutorial on variance analysis, flexible budgets, and overhead allocation. View Details
Keywords: Mathematical Methods
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"Variance Analysis Tutorial." Harvard Business School Tutorial 104-709, March 2004.
  • March 2004
  • Tutorial

HBS Quantitative Analysis Course

By: Janice H. Hammond
Keywords: Mathematical Methods
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"HBS Quantitative Analysis Course." Harvard Business School Tutorial 604-702, March 2004.
  • 1977
  • Article

On the Joint Distribution of Left- and Right-sided Outliner Statistics

By: André Perold and D. M. Hawkins
Keywords: Mathematical Methods
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Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.
  • July 2023
  • Article

Design and Analysis of Switchback Experiments

By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted... View Details
Keywords: Switchback Experiments; Design; Analysis; Mathematical Methods
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Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Management Science 69, no. 7 (July 2023): 3759–3777.
  • January 1997
  • Background Note

Simulation as a Decision Aid

By: Roy D. Shapiro
A brief introduction to simulation--what it is, why it's used, etc. Meant to set context for a first class on simulation. A rewritten version of an earlier note. View Details
Keywords: Mathematical Methods; Decision Making
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Shapiro, Roy D. "Simulation as a Decision Aid." Harvard Business School Background Note 697-062, January 1997.
  • 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.
  • 1985
  • Chapter

The Role of Contingent Claims Analysis in Corporate Finance

By: Scott P. Mason and Robert C. Merton
Keywords: Mathematical Methods; Corporate Finance
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Mason, Scott P., and Robert C. Merton. "The Role of Contingent Claims Analysis in Corporate Finance." In Recent Advances in Corporate Finance, edited by E. I. Altman and M. G. Subrahmanyam. Homewood, IL: Richard D. Irwin, 1985.
  • 1999
  • Chapter

Interest Rate Rules in an Estimated Sticky Price Model

By: Julio J. Rotemberg and Michael Woodford
Keywords: Interest Rates; Mathematical Methods
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Rotemberg, Julio J., and Michael Woodford. "Interest Rate Rules in an Estimated Sticky Price Model." In Monetary Policy Rules, edited by John B. Taylor. Chicago: University of Chicago Press, 1999.
  • 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.)
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