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  • All HBS Web  (1,960)
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  • August 2006
  • Article

Confidence Intervals for Probabilities of Default

By: Samuel G. Hanson and Til Schuermann
In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation... View Details
Keywords: Credit Risk; Bootstrap; Mathematical Methods; Credit; Risk Management
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Hanson, Samuel G., and Til Schuermann. "Confidence Intervals for Probabilities of Default." Journal of Banking & Finance 30, no. 8 (August 2006).
  • July–August 2023
  • Article

Demand Learning and Pricing for Varying Assortments

By: Kris Ferreira and Emily Mower
Problem Definition: We consider the problem of demand learning and pricing for retailers who offer assortments of substitutable products that change frequently, e.g., due to limited inventory, perishable or time-sensitive products, or the retailer’s desire to... View Details
Keywords: Experiments; Pricing And Revenue Management; Retailing; Demand Estimation; Pricing Algorithm; Marketing; Price; Demand and Consumers; Mathematical Methods
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Ferreira, Kris, and Emily Mower. "Demand Learning and Pricing for Varying Assortments." Manufacturing & Service Operations Management 25, no. 4 (July–August 2023): 1227–1244. (Finalist, Practice-Based Research Competition, MSOM (2021) and Finalist, Revenue Management & Pricing Section Practice Award, INFORMS (2019).)
  • July 1990
  • Background Note

Perceptual Mapping: A Manager's Guide

By: Robert J. Dolan
Describes the perceptual mapping technique in a non-technical fashion. The procedure is useful for the depiction of the structure of the market. Discusses alternative methods, presents examples of each, and shows how the maps can be used in marketing decision making. View Details
Keywords: Mathematical Methods; Industry Structures; Marketing
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Dolan, Robert J. "Perceptual Mapping: A Manager's Guide." Harvard Business School Background Note 590-121, July 1990.
  • 1999
  • Other Unpublished Work

Estimating Industry Multiples

By: Malcolm Baker and R. S. Ruback
We analyze industry multiples for the S&P 500 in 1995. We use Gibbs sampling to estimate simultaneously the error specification and small sample minimum variance multiples for 22 industries. In addition, we consider the performance of four common multiples: the simple... View Details
Keywords: Management Analysis, Tools, and Techniques; Performance; Mathematical Methods
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Baker, Malcolm, and R. S. Ruback. "Estimating Industry Multiples." 1999.
  • 18 Sep 2019
  • Working Paper Summaries

Using Models to Persuade

Keywords: by Joshua Schwartzstein and Adi Sunderam
  • September 1993 (Revised August 2011)
  • Exercise

ExtendSim® Simulation Exercises in Process Analysis (A)

By: Roy D. Shapiro
First set of exercises meant to be used with ExtendSim, a simulation system created by Imagine That, Inc. of San Jose, California. These exercises allow students to investigate the impact of variable processing times on the performance of simple in-line processes.... View Details
Keywords: Operations; Business Processes; Performance; Mathematical Methods
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Shapiro, Roy D. "ExtendSim® Simulation Exercises in Process Analysis (A)." Harvard Business School Exercise 694-039, September 1993. (Revised August 2011.)
  • 1 Dec 1998
  • Conference Presentation

An Introduction to Mixed Models in SAS

By: William B. Simpson
Keywords: Applications and Software; Mathematical Methods
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Simpson, William B. "An Introduction to Mixed Models in SAS." Boston Area SAS Users Group, Boston, MA, December 1, 1998.
  • June 2008
  • Supplement

Marie Trellu-Kane at Unis-Cite

By: Michel Anteby and Julie Battilana
Video supplement to Marie Trellu-Kane at Unis-Cite (A). View Details
Keywords: Social Enterprise; Organizational Design; Mathematical Methods; Paris
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Anteby, Michel, and Julie Battilana. "Marie Trellu-Kane at Unis-Cite." Harvard Business School Video Supplement 408-709, June 2008.
  • 1996
  • Thesis

Limits on Interest Rate Rules in Macroeconomic Models Governed by Price Stickiness and Rational Expectations

By: William R. Kerr
Keywords: Interest Rates; Macroeconomics; Mathematical Methods
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Kerr, William R. "Limits on Interest Rate Rules in Macroeconomic Models Governed by Price Stickiness and Rational Expectations." Thesis, University of Virginia, 1996.
  • August 1991
  • Background Note

Industrial Market Research: Beta Test Site Management

By: Robert J. Dolan
Describes the role of BETA tests in the new product development process and presents guidelines for effective test program development. View Details
Keywords: Product Development; Mathematical Methods; Marketing
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Dolan, Robert J. "Industrial Market Research: Beta Test Site Management." Harvard Business School Background Note 592-010, August 1991.
  • 2023
  • Working Paper

Design-Based Inference for Multi-arm Bandits

By: Dae Woong Ham, Iavor I. Bojinov, Michael Lindon and Martin Tingley
Multi-arm bandits are gaining popularity as they enable real-world sequential decision-making across application areas, including clinical trials, recommender systems, and online decision-making. Consequently, there is an increased desire to use the available... View Details
Keywords: Analytics and Data Science; Mathematical Methods
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Ham, Dae Woong, Iavor I. Bojinov, Michael Lindon, and Martin Tingley. "Design-Based Inference for Multi-arm Bandits." Harvard Business School Working Paper, No. 24-056, March 2024.
  • 2023
  • Working Paper

Distributionally Robust Causal Inference with Observational Data

By: Dimitris Bertsimas, Kosuke Imai and Michael Lingzhi Li
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first... View Details
Keywords: AI and Machine Learning; Mathematical Methods
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Bertsimas, Dimitris, Kosuke Imai, and Michael Lingzhi Li. "Distributionally Robust Causal Inference with Observational Data." Working Paper, February 2023.
  • 2023
  • Article

On Minimizing the Impact of Dataset Shifts on Actionable Explanations

By: Anna P. Meyer, Dan Ley, Suraj Srinivas and Himabindu Lakkaraju
The Right to Explanation is an important regulatory principle that allows individuals to request actionable explanations for algorithmic decisions. However, several technical challenges arise when providing such actionable explanations in practice. For instance, models... View Details
Keywords: Mathematical Methods; Analytics and Data Science
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Meyer, Anna P., Dan Ley, Suraj Srinivas, and Himabindu Lakkaraju. "On Minimizing the Impact of Dataset Shifts on Actionable Explanations." Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI) 39th (2023): 1434–1444.
  • 2017
  • Working Paper

Investment Timing with Costly Search for Financing

By: Samuel Antill
I develop a dynamic model of investment timing in which firms must first choose when to search for external financing. Search is costly and the arrival of investors is uncertain, leading to delay in financing and investment. Depending on parameters, my model can... View Details
Keywords: Real Options; Search And Bargaining; Time-varying Financial Conditions; Investment; Venture Capital; Mathematical Methods
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Antill, Samuel. "Investment Timing with Costly Search for Financing." Working Paper, December 2017.
  • January 2011
  • Teaching Note

AIC Netbooks: Optimizing Product Assembly (Brief Case)

By: Steven C. Wheelwright and Sunru Yong
Teaching Note for 4245. View Details
Keywords: Performance Management; Quantitative Analysis; Manufacturing; Production Planning; Production Management; Production; Mathematical Methods; Performance Evaluation; Planning; Manufacturing Industry
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Wheelwright, Steven C., and Sunru Yong. "AIC Netbooks: Optimizing Product Assembly (Brief Case)." Harvard Business School Teaching Note 114-246, January 2011.
  • 1981
  • Chapter

Productivity Measurement at the Level of the Firm: An Application within the Service Industry

By: Hirotaka Takeuchi
Keywords: Performance Productivity; Measurement and Metrics; Mathematical Methods; Service Industry
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Takeuchi, Hirotaka. "Productivity Measurement at the Level of the Firm: An Application within the Service Industry." In Productivity Analysis at the Firm Level, edited by Ali Dogramaci and Nabil R. Adam. Martinus Nijhoff Publishers, 1981.
  • November 1989 (Revised March 1992)
  • Background Note

Concept Testing

By: Robert J. Dolan
Describes concept testing products. Presents guidelines for effective design, execution, and interpretation of test procedures. Discusses limitations of these techniques and sets out the situations for which they are appropriate. View Details
Keywords: Marketing; Mathematical Methods; Forecasting and Prediction
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Dolan, Robert J. "Concept Testing." Harvard Business School Background Note 590-063, November 1989. (Revised March 1992.)
  • Other Unpublished Work

A Technique to Estimate Retail Demand and Lost Sales

By: A. Raman and Giulio Zotteri
Keywords: Mathematical Methods; Demand and Consumers; Sales; Retail Industry
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Raman, A., and Giulio Zotteri. "A Technique to Estimate Retail Demand and Lost Sales."
  • 2018
  • Working Paper

Full Substitutability

By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of... View Details
Keywords: Substitutability; Mathematical Methods; Auctions; Market Design
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Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Harvard Business School Working Paper, No. 19-016.
  • Article

Testing Substitutability

By: John William Hatfield, Nicole Immorlica and Scott Duke Kominers
We provide an algorithm for testing the substitutability of a length-N preference relation over a set of contracts X in time O(|X|3⋅N3). Access to the preference relation is essential for this result: We show that a substitutability-testing algorithm with access only... View Details
Keywords: Substitutability; Matching; Communication Complexity; Preference Elicitation; Marketplace Matching; Communication; Mathematical Methods; Economics
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Hatfield, John William, Nicole Immorlica, and Scott Duke Kominers. "Testing Substitutability." Games and Economic Behavior 75, no. 2 (July 2012): 639–645.
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