Filter Results:
(838)
Show Results For
- All HBS Web
(838)
- News (77)
- Research (639)
- Events (11)
- Multimedia (4)
- Faculty Publications (636)
Show Results For
- All HBS Web
(838)
- News (77)
- Research (639)
- Events (11)
- Multimedia (4)
- Faculty Publications (636)
- January 1982
- Background Note
Sharing Costs: Internal Telephone Billing Rates
By: Elon Kohlberg
Kohlberg, Elon. "Sharing Costs: Internal Telephone Billing Rates." Harvard Business School Background Note 182-109, January 1982.
- 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
Merton's Economics Research Wins Nobel Prize
evaluation began when he was a graduate student in applied mathematics at the California Institute of Technology and intensified in the late 1960s, when he went to MIT to study economics under Nobel Laureate Paul Samuelson. At MIT, he... 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
- 1970
- Dissertation
Analytical Optimal Control Theory as Applied to Stochastic and Non-Stochastic Economics
By: Robert C. Merton
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
Khanna, Tarun, and Jan W. Rivkin. "Math Tools for Strategists." Harvard Business School Background Note 718-477, January 2018.
- 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
Dolan, Robert J. "Note on Low-Tech Marketing Math." Harvard Business School Background Note 599-011, December 1998.
- 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
- Forthcoming
- Article
Branch-and-Price for Prescriptive Contagion Analytics
By: Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé and Kai Wang
Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details
Jacquillat, Alexandre, Michael Lingzhi Li, Martin Ramé, and Kai Wang. "Branch-and-Price for Prescriptive Contagion Analytics." Operations Research (forthcoming). (Pre-published online March 13, 2024.)
- 2020
- Article
Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion
By: Dimitris Bertsimas and Michael Lingzhi Li
We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the... View Details
Keywords: Mathematical Methods
Bertsimas, Dimitris, and Michael Lingzhi Li. "Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion." Journal of Machine Learning Research 21, no. 1 (2020).
- Article
How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
We explain when and how staggered difference-in-differences regression estimators, commonly applied to assess the impact of policy changes, are biased. These biases are likely to be relevant for a large portion of research settings in finance, accounting, and law that... View Details
Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" Journal of Financial Economics 144, no. 2 (May 2022): 370–395. (Editor's Choice, May 2022; Jensen Prize, First Place, June 2023.)
- Mar 2021
- Conference Presentation
Descent-to-Delete: Gradient-Based Methods for Machine Unlearning
By: Seth Neel, Aaron Leon Roth and Saeed Sharifi-Malvajerdi
We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial updates while promising both... View Details
Neel, Seth, Aaron Leon Roth, and Saeed Sharifi-Malvajerdi. "Descent-to-Delete: Gradient-Based Methods for Machine Unlearning." Paper presented at the 32nd Algorithmic Learning Theory Conference, March 2021.
- Article
Oracle Efficient Private Non-Convex Optimization
By: Seth Neel, Aaron Leon Roth, Giuseppe Vietri and Zhiwei Steven Wu
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it.... View Details
Neel, Seth, Aaron Leon Roth, Giuseppe Vietri, and Zhiwei Steven Wu. "Oracle Efficient Private Non-Convex Optimization." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
- Article
Aztec Castles and the dP3 Quiver
By: Megan Leoni, Gregg Musiker, Seth Neel and Paxton Turner
Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 (dP3) quiver and geometric properties of its corresponding brane tiling. In... View Details
Leoni, Megan, Gregg Musiker, Seth Neel, and Paxton Turner. "Aztec Castles and the dP3 Quiver." Journal of Physics A: Mathematical and Theoretical 47, no. 47 (November 28, 2014).
- 2021
- Working Paper
How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
Difference-in-differences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the... View Details
Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" European Corporate Governance Institute Finance Working Paper, No. 736/2021, February 2021. (Harvard Business School Working Paper, No. 21-112, April 2021.)
- 1990
- Chapter
Refinement of Nash Equilibrium: The Main Ideas
By: E. Kohlberg
Keywords: Mathematical Methods
Kohlberg, E. "Refinement of Nash Equilibrium: The Main Ideas." In Game Theory and Applications, edited by T. Ichiishi, A. Neyman, and Y. Tauman. San Diego: Academic Press, 1990.
- Article
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80
By: Noam D. Elkies and Scott Duke Kominers
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80." Proceedings of the American Mathematical Society 138, no. 1 (January 2010): 105–108.