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- Faculty Publications (568)
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- All HBS Web (618)
- Faculty Publications (568)
- November 2004 (Revised April 2005)
- Background Note
Math for Strategists
By: Tarun Khanna and Jan W. Rivkin
Great strategists rely heavily on numbers as they go about their work. Offers an overview of the high- and low-brow quantitative tools that students encounter during the Strategy course. The class explores high-brow tools in detail; the focus here is on low-brow... View Details
Khanna, Tarun, and Jan W. Rivkin. "Math for Strategists." Harvard Business School Background Note 705-433, November 2004. (Revised April 2005.)
- fall 1973
- Article
Statistical Sampling in Auditing with Auxiliary Information Estimators
By: Robert S. Kaplan
Kaplan, Robert S. "Statistical Sampling in Auditing with Auxiliary Information Estimators." Journal of Accounting Research 11 (fall 1973): 238–258.
- March 1992 (Revised June 1992)
- Background Note
Strategic Industry Model: Emergent Technologies
By: Robert J. Dolan
Describes computer model and output from conjoint analysis and perceptual mapping for product line planning. View Details
Dolan, Robert J. "Strategic Industry Model: Emergent Technologies." Harvard Business School Background Note 592-086, March 1992. (Revised June 1992.)
- 1985
- Chapter
The Role of Contingent Claims Analysis in Corporate Finance
By: Scott P. Mason and Robert C. Merton
- 1999
- Chapter
Interest Rate Rules in an Estimated Sticky Price Model
By: Julio J. Rotemberg and Michael Woodford
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
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
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
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
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
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
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
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
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
Wheeler, Michael A. Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America. New York, NY: W. W. Norton & Company, 1976.
- 2024
- Working Paper
Winner Take All: Exploiting Asymmetry in Factorial Designs
By: Matthew DosSantos DiSorbo, Iavor I. Bojinov and Fiammetta Menchetti
Researchers and practitioners have embraced factorial experiments to simultaneously test multiple treatments, each with different levels. With the rise of technologies like Generative AI, factorial experimentation has become even more accessible: it is easier than ever... View Details
Keywords: Factorial Designs; Fisher Randomizations; Rank Estimators; Employer Interventions; Causal Inference; Mathematical Methods; Performance Improvement
DosSantos DiSorbo, Matthew, Iavor I. Bojinov, and Fiammetta Menchetti. "Winner Take All: Exploiting Asymmetry in Factorial Designs." Harvard Business School Working Paper, No. 24-075, June 2024.
- September 2021
- Article
Diagnostic Bubbles
By: Pedro Bordalo, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We introduce diagnostic expectations into a standard setting of price formation in which investors learn about the fundamental value of an asset and trade it. We study the interaction of diagnostic expectations with two well-known mechanisms: learning from prices and... View Details
Bordalo, Pedro, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "Diagnostic Bubbles." Journal of Financial Economics 141, no. 3 (September 2021).
- 14 Aug 2017
- Conference Presentation
A Convex Framework for Fair Regression
By: Richard Berk, Hoda Heidari, Shahin Jabbari, Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel and Aaron Roth
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the range from notions of group fairness to strong individual fairness. By varying... View Details
Berk, Richard, Hoda Heidari, Shahin Jabbari, Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel, and Aaron Roth. "A Convex Framework for Fair Regression." Paper presented at the 4th Workshop on Fairness, Accountability, and Transparency in Machine Learning, Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD), August 14, 2017.
- Article
A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects
By: Edward McFowland III, Sandeep Gangarapu, Ravi Bapna and Tianshu Sun
We define a prescriptive analytics framework that addresses the needs of a constrained decision-maker facing, ex ante, unknown costs and benefits of multiple policy levers. The framework is general in nature and can be deployed in any utility maximizing context, public... View Details
Keywords: Prescriptive Analytics; Heterogeneous Treatment Effects; Optimization; Observed Rank Utility Condition (OUR); Between-treatment Heterogeneity; Machine Learning; Decision Making; Analysis; Mathematical Methods
McFowland III, Edward, Sandeep Gangarapu, Ravi Bapna, and Tianshu Sun. "A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects." MIS Quarterly 45, no. 4 (December 2021): 1807–1832.
- 1995
- Chapter
Dynamic General Equilibrium Models with Imperfectly Competitive Product Markets
By: Julio J. Rotemberg and Michael Woodford