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Show Results For
-
All HBS Web
(833)
- News (77)
- Research (636)
- Events (11)
- Multimedia (4)
- Faculty Publications (631)
- May 2000
- Article
Maxmin Expected Utility over Savage Acts with a Set of Priors
By: Ramon Casadesus-Masanell, Peter Klibanoff and Emre Ozdenoren
This paper provides an axiomatic foundation for a maxmin expected utility over a set of priors (MMEU) decision rule in an environment where the elements of choice are Savage acts. This characterization complements the original axiomatizations of MMEU developed in a...
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Keywords:
Uncertainty Aversion;
Ambiguity;
Expected Utility;
Set Of Priors;
Knightian Uncertainty;
Decision Making;
Game Theory;
Risk and Uncertainty;
Mathematical Methods
Casadesus-Masanell, Ramon, Peter Klibanoff, and Emre Ozdenoren. "Maxmin Expected Utility over Savage Acts with a Set of Priors." Journal of Economic Theory 92, no. 1 (May 2000): 35–65.
- 01 Sep 2009
- News
Of Value and Values
of investment management. “I think that vote captured a powerful tension inside the students,” she remarks. “They have plenty of mathematical and financial models to support the point of view that restricting the size of an ‘investable...
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- 2024
- Working Paper
Empirical Guidance: Data Processing and Analysis with Applications in Stata, R, and Python
By: Melissa Ouellet and Michael W. Toffel
This paper describes a range of best practices to compile and analyze datasets, and includes some examples in Stata, R, and Python. It is meant to serve as a reference for those getting started in econometrics, and especially those seeking to conduct data analyses in...
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Keywords:
Empirical Methods;
Empirical Operations;
Statistical Methods And Machine Learning;
Statistical Interferences;
Research Analysts;
Analytics and Data Science;
Mathematical Methods
Ouellet, Melissa, and Michael W. Toffel. "Empirical Guidance: Data Processing and Analysis with Applications in Stata, R, and Python." Harvard Business School Working Paper, No. 25-010, August 2024.
- 2021
- Working Paper
Impact Investing: A Theory of Financing Social Enterprises
By: Benjamin N. Roth
I present a model of financing social enterprises to delineate the role of impact investors relative to “pure” philanthropists. I characterize the optimal scale and structure of a social enterprise when financed by grants, and when financed by investments. Impact...
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Roth, Benjamin N. "Impact Investing: A Theory of Financing Social Enterprises." Harvard Business School Working Paper, No. 20-078, February 2020. (Revised June 2021.)
- Article
Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs
By: Y. Grushka-Cockayne, K. C. Lichtendahl, V.R.R. Jose and R.L. Winkler
From forecasting competitions to conditional value-at-risk requirements, the use of multiple quantile assessments is growing in practice. To evaluate them, we use a rule from the general class of proper scoring rules for a forecaster’s multiple quantiles of a single...
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Grushka-Cockayne, Y., K. C. Lichtendahl, V.R.R. Jose, and R.L. Winkler. "Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs." Operations Research 65, no. 3 (May–June 2017): 712–728.
- January 2000
- Article
Maxmin Expected Utility through Statewise Combinations
By: Ramon Casadesus-Masanell, Peter Klibanoff and Emre Ozdenoren
This paper provides an axiomatic foundation for a maxmin expected utility over a set of priors (MMEU) decision rule in an environment where the elements of choice are Savage acts. The key axioms are stated using statewise combinations as in Gul (1992).
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Casadesus-Masanell, Ramon, Peter Klibanoff, and Emre Ozdenoren. "Maxmin Expected Utility through Statewise Combinations." Economics Letters 66, no. 1 (January 2000): 49–54.
- March 2016 (Revised January 2020)
- Teaching Note
Behavioural Insights Team (A) and (B)
By: Michael Luca and Patrick Rooney
The Behavioural Insights Team case introduces students to the concept of choice architecture and the value of experimental methods (sometimes called A/B testing) within organizational contexts. The exercise provides an opportunity for students to apply these principles...
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- March 2011 (Revised April 2021)
- Case
The Whiz Kids
By: Tom Nicholas and David Chen
In October 1945, Henry Ford II received a telegram in his office at the Ford Motor Company in Dearborn, Michigan written by Charles "Tex" Thornton, a U.S. Air Force colonel. The telegram presented an opportunity for Ford to deploy a system of statistical control which...
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Keywords:
Ford Motor Company;
Statistical Control;
Management Systems;
Accounting;
Operations;
Strategy;
Mathematical Methods;
Auto Industry;
United States
Nicholas, Tom, and David Chen. "The Whiz Kids." Harvard Business School Case 811-042, March 2011. (Revised April 2021.)
- Working Paper
Group Fairness in Dynamic Refugee Assignment
By: Daniel Freund, Thodoris Lykouris, Elisabeth Paulson, Bradley Sturt and Wentao Weng
Ensuring that refugees and asylum seekers thrive (e.g., find employment) in their host countries is a profound humanitarian goal, and a primary driver of employment is the geographic
location within a host country to which the refugee or asylum seeker is...
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Freund, Daniel, Thodoris Lykouris, Elisabeth Paulson, Bradley Sturt, and Wentao Weng. "Group Fairness in Dynamic Refugee Assignment." Harvard Business School Working Paper, No. 23-047, February 2023.
- August 2003 (Revised May 2009)
- Background Note
Basic Venture Capital Formula, The
By: William A. Sahlman and Matthew Willis
Briefly summarizes the process that venture capitalists use to analyze high-risk, long-term investments. Contains information on methods that can be used to calculate valuation, share price, percent ownership, implied valuation, dilution, and option pools.
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Sahlman, William A., and Matthew Willis. "Basic Venture Capital Formula, The." Harvard Business School Background Note 804-042, August 2003. (Revised May 2009.)
- 2022
- Article
Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods.
By: Chirag Agarwal, Marinka Zitnik and Himabindu Lakkaraju
As Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes critical to ensure that the stakeholders understand the rationale behind their predictions. While several GNN explanation methods have been proposed recently, there has...
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Keywords:
Graph Neural Networks;
Explanation Methods;
Mathematical Methods;
Framework;
Theory;
Analysis
Agarwal, Chirag, Marinka Zitnik, and Himabindu Lakkaraju. "Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
- Article
Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses
By: Kaivalya Rawal and Himabindu Lakkaraju
As predictive models are increasingly being deployed in high-stakes decision-making, there has been a lot of interest in developing algorithms which can provide recourses to affected individuals. While developing such tools is important, it is even more critical to...
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Rawal, Kaivalya, and Himabindu Lakkaraju. "Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses." Advances in Neural Information Processing Systems (NeurIPS) 33 (2020).
- October 2020
- Article
Comparative Statics for Size-Dependent Discounts in Matching Markets
By: David Delacretaz, Scott Duke Kominers and Alexandru Nichifor
We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side...
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Keywords:
Size-dependent Discounts;
Path-independence;
Respect For Improvements;
Market Design;
Mathematical Methods
Delacretaz, David, Scott Duke Kominers, and Alexandru Nichifor. "Comparative Statics for Size-Dependent Discounts in Matching Markets." Journal of Mathematical Economics 90 (October 2020): 127–131.
- September 2019
- Article
Optimizing Reserves in School Choice: A Dynamic Programming Approach
By: Franklyn Wang, Ravi Jagadeesan and Scott Duke Kominers
We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a...
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Wang, Franklyn, Ravi Jagadeesan, and Scott Duke Kominers. "Optimizing Reserves in School Choice: A Dynamic Programming Approach." Operations Research Letters 47, no. 5 (September 2019): 438–446.
- Article
Distributionally Robust Optimization and Its Tractable Approximations
By: Joel Goh and Melvyn Sim
In this paper we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more...
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Goh, Joel, and Melvyn Sim. "Distributionally Robust Optimization and Its Tractable Approximations." Operations Research 58, no. 4 (pt.1) (July–August 2010): 902–917.
- June 2007
- Tutorial
Congruence Model Tutorial
By: Christopher Marquis and Alison Comings
Utilizes Beer & Tushman's SMA: Microelectronic Products Division (A) case to explore O'Reilly and Tushman's congruence model. Participants learn about the model through a series of video presentations and become familar with the problems facing SMA through an...
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- spring 1973
- Article
A Stochastic Model for Auditing
By: Robert S. Kaplan
Kaplan, Robert S. "A Stochastic Model for Auditing." Journal of Accounting Research 11 (spring 1973): 38–46.