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(841)
- News (79)
- Research (640)
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- Faculty Publications (635)
Show Results For
- All HBS Web
(841)
- News (79)
- Research (640)
- Events (14)
- Multimedia (4)
- Faculty Publications (635)
- 2002
- Chapter
Future Possibilities in Finance Theory and Finance Practice
By: Robert C. Merton
Merton, Robert C. "Future Possibilities in Finance Theory and Finance Practice." In Mathematical Finance - Bachelier Congress 2000, edited by H. Geman, D. Madan, S. Pliska, and T. Vorst. Berlin: Springer-Verlag, 2002. (Was HBS Working Paper 01-030.)
- September 1976 (Revised June 1977)
- Background Note
Assessing Certainty Equivalents by Assessing Preference for Consequences
By: Paul A. Vatter
Vatter, Paul A. "Assessing Certainty Equivalents by Assessing Preference for Consequences." Harvard Business School Background Note 177-038, September 1976. (Revised June 1977.)
- 01 Dec 1997
- News
"Economists are puzzle solvers..."
(I've always been a car buff!) when I was ten. I can remember going with my dad to the stockbroker's and sitting there watching the NYSE and AMEX tapes, learning all the companies' symbols. And when I was in graduate school in applied View Details
- 16 Oct 2019
- News
The Road to Impact
increasing the organization’s visibility. “We may have discovered a better way to teach young kids mathematics or to teach non-English speakers how to read English in third grade, or how to better inhibit suicidal patients from taking... View Details
- 01 Oct 1998
- News
Merton Named University Professor
mathematics from Columbia University in 1966, Merton studied applied mathematics at the California Institute of Technology and earned an MS in 1967. In 1970 he completed a Ph.D. in economics at MIT and... View Details
- Profile
Sid Shenai
For most of his life, Sid Shenai had pursued a single goal: to be a mathematical physicist. At Harvard, Sid finished his required courses early and participated in graduate level research. But his path toward a Ph.D was interrupted by a... View Details
- April 1990
- Case
Clark Material Handling Group-Overseas: Brazilian Product Strategy (A&B) (Condensed)
By: Robert J. Dolan
Assumes some knowledge of conjoint analysis. Permits analysis of basic results and dynamic market simulations in one class session. View Details
Dolan, Robert J. "Clark Material Handling Group-Overseas: Brazilian Product Strategy (A&B) (Condensed)." Harvard Business School Case 590-081, April 1990.
- 06 Apr 2020
- Working Paper Summaries
A General Theory of Identification
Keywords: by Iavor Bojinov and Guillaume Basse
- 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
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
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
Bell, David E. "Why Preference Curves are Useful for Risky Decisions." Harvard Business School Background Note 183-030, July 1982. (Revised March 1984.)
- 1972
- Chapter
Random Walks and Technical Theories: Some Additional Evidence
By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
Benington, George A., and Michael C. Jensen. "Random Walks and Technical Theories: Some Additional Evidence." In Security Evaluation and Portfolio Analysis, edited by E. Elton and M. Gruber. Prentice Hall, 1972. (Also published in Journal of Finance (May 1970) and Investment Management: Some Readings, J. Lorie and R. Brealey, Editors (Praeger Publishers, 1972).)
- 1979
- Article
An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem
By: C. Blair and A. E. Roth
Keywords: Mathematical Methods
Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.
- January 1975
- Article
A Lattice Fixed-Point Theorem with Constraints
By: A. E. Roth
Keywords: Mathematical Methods
Roth, A. E. "A Lattice Fixed-Point Theorem with Constraints." Bulletin of the American Mathematical Society 81 (January 1975): 136–138.
- September–October 2023
- Article
Interpretable Matrix Completion: A Discrete Optimization Approach
By: Dimitris Bertsimas and Michael Lingzhi Li
We consider the problem of matrix completion on an n × m matrix. We introduce the problem of interpretable matrix completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be... View Details
Keywords: Mathematical Methods
Bertsimas, Dimitris, and Michael Lingzhi Li. "Interpretable Matrix Completion: A Discrete Optimization Approach." INFORMS Journal on Computing 35, no. 5 (September–October 2023): 952–965.
- 2022
- Article
Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis.
By: Martin Pawelczyk, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay and Himabindu Lakkaraju
As machine learning (ML) models become more widely deployed in high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a... View Details
Keywords: Machine Learning Models; Counterfactual Explanations; Adversarial Examples; Mathematical Methods
Pawelczyk, Martin, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay, and Himabindu Lakkaraju. "Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
- November 2021
- Article
Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective
By: Iavor Bojinov, Ashesh Rambachan and Neil Shephard
In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative... View Details
Keywords: Panel Data; Dynamic Causal Effects; Potential Outcomes; Finite Population; Nonparametric; Mathematical Methods
Bojinov, Iavor, Ashesh Rambachan, and Neil Shephard. "Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective." Quantitative Economics 12, no. 4 (November 2021): 1171–1196.
- 2018
- Working Paper
Bundling Incentives in (Many-to-Many) Matching with Contracts
By: Jonathan Ma and Scott Duke Kominers
In many-to-many matching with contracts, the way in which contracts are specified can affect the set of stable equilibrium outcomes. Consequently, agents may be incentivized to modify the set of contracts upfront. We consider one simple way in which agents may do so:... View Details
Keywords: Matching With Contracts; Contract Design; Bundling-proofness; Substitutability; Mathematical Methods
Ma, Jonathan, and Scott Duke Kominers. "Bundling Incentives in (Many-to-Many) Matching with Contracts." Harvard Business School Working Paper, No. 19-011, August 2018.
- 2011
- Chapter
Fundamental Data Anomalies
By: Ian D. Gow
Gow, Ian D. "Fundamental Data Anomalies." Chap. 5 in The Handbook of Equity Market Anomalies: Translating Market Inefficiencies into Effective Investment Strategies, edited by Len Zacks, 117–128. John Wiley & Sons, 2011.
- November 1990 (Revised November 1992)
- Background Note
Note on Linear Programming
Gives an elementary introduction to formulating linear programming models and interpreting linear programmings output. Other aspects of linear programming are discussed briefly. View Details
Keywords: Mathematical Methods
Eckstein, Jonathan. "Note on Linear Programming." Harvard Business School Background Note 191-085, November 1990. (Revised November 1992.)