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  • All HBS Web  (1,959)
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  • 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.
  • June 1994
  • Article

Influence of Mathematical Models in Finance on Practice: Past, Present and Future

By: Robert C. Merton
Keywords: Mathematical Methods; Finance
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Merton, Robert C. "Influence of Mathematical Models in Finance on Practice: Past, Present and Future." Series A. Philosophical Transactions of the Royal Society of London, Series A, Physical Sciences and Engineering 347 (June 1994): 451–463. (Reprinted in Financial Practice and Education, spring 1995.)
  • 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.
  • 18 Nov 2016
  • Conference Presentation

Rawlsian Fairness for Machine Learning

By: Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
Motivated by concerns that automated decision-making procedures can unintentionally lead to discriminatory behavior, we study a technical definition of fairness modeled after John Rawls' notion of "fair equality of opportunity". In the context of a simple model of... View Details
Keywords: Machine Learning; Algorithms; Fairness; Decision Making; Mathematical Methods
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Joseph, Matthew, Michael J. Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Rawlsian Fairness for Machine Learning." Paper presented at the 3rd Workshop on Fairness, Accountability, and Transparency in Machine Learning, Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD), November 18, 2016.
  • 2008
  • Chapter

Assessing Creativity and Its Antecedents: An Exploration of the Componential Theory of Creativity

By: T. M. Amabile and Jennifer Mueller
Keywords: Creativity; Mathematical Methods; Theory
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Amabile, T. M., and Jennifer Mueller. "Assessing Creativity and Its Antecedents: An Exploration of the Componential Theory of Creativity." In Handbook of Organizational Creativity, edited by Jing Zhou and Christina E. Shalley. Lawrence Erlbaum Associates, 2008.
  • March 1999 (Revised December 2001)
  • Background Note

Analyzing Consumer Preferences

By: Robert J. Dolan
Presents a non-traditional description of the conjoint analysis methodology. Discusses the process by which a study is done and cites areas of application. View Details
Keywords: Marketing; Mathematical Methods; Product Marketing
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Dolan, Robert J. "Analyzing Consumer Preferences." Harvard Business School Background Note 599-112, March 1999. (Revised December 2001.)
  • July 2002
  • Article

The Economist As Engineer: Game Theory, Experimental Economics and Computation As Tools of Design Economics

By: Alvin E Roth
Keywords: Game Theory; Economics; Mathematical Methods; Design
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Roth, Alvin E. "The Economist As Engineer: Game Theory, Experimental Economics and Computation As Tools of Design Economics." Econometrica 70, no. 4 (July 2002): 1341–1378.
  • 1982
  • Chapter

On the Mathematics and Economic Assumptions of Continuous-Time Financial Models

By: Robert C. Merton
Keywords: Mathematical Methods; Economics; Finance
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Merton, Robert C. "On the Mathematics and Economic Assumptions of Continuous-Time Financial Models." In Financial Economics: Essays in Honor of Paul Cootner, edited by W. F. Sharpe and C. M. Cootner. Englewood Cliffs, NJ: Prentice Hall, 1982. (Chapter 3 in Continuous-Time Finance.)
  • 2006
  • Book

Service Productivity Management: Improving Service Performance Using Data Envelopment Analysis

By: H. David Sherman and Joe Zhu
Here is an in-depth guide to the most powerful available benchmarking technique for improving service organization performance—Data Envelopment Analysis (DEA). The book outlines DEA as a benchmarking technique, identifies high cost service units, isolates specific... View Details
Keywords: Data Envelopment Analysis; Economics; Operations; Mathematical Methods
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Sherman, H. David, and Joe Zhu. Service Productivity Management: Improving Service Performance Using Data Envelopment Analysis. Boston, MA: Springer, 2006.
  • 1991
  • Chapter

An Economic Approach to the Study of Bargaining

By: A. E. Roth
Keywords: Negotiation; Economics; Mathematical Methods
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Roth, A. E. "An Economic Approach to the Study of Bargaining." In Handbook of Negotiation Research. Vol. 3, edited by M. H. Bazerman, R. J. Lewicki, and B. H. Sheppard, 35–67. Research on Negotiation in Organizations. JAI Press, 1991.
  • July 1982 (Revised March 1984)
  • Background Note

Why Preference Curves are Useful for Risky Decisions

By: David E. Bell
Keywords: Mathematical Methods; Decision Making
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Bell, David E. "Why Preference Curves are Useful for Risky Decisions." Harvard Business School Background Note 183-030, July 1982. (Revised March 1984.)
  • 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.
  • 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.)
  • 08 Nov 2024
  • HBS Case

What Wartime Service Taught These Historic Leaders

growing—with HBS Research Assistant Shirley Sun. Here, Simons discusses three leaders whose service left a powerful mark, leading to their own success. Business leaders might learn some important lessons from their experiences, he says.... View Details
Keywords: by Avery Forman; Entertainment & Recreation
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