Mathematical Methods - Publications - Faculty & Research - Harvard Business School

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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... View Details

Keywords: Uncertainty Aversion; Ambiguity; Expected Utility; Set Of Priors; Knightian Uncertainty; Decision Making; Game Theory; Risk and Uncertainty; Mathematical Methods

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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

2024
Working Paper

Bootstrap Diagnostics for Irregular Estimators

By: Isaiah Andrews and Jesse M. Shapiro

Empirical researchers frequently rely on normal approximations in order to summarize and communicate uncertainty about their findings to their scientific audience. When such approximations are unreliable, they can lead the audience to make misguided decisions. We... View Details

Keywords: Mathematical Methods; Decision Choices and Conditions

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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

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

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

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

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

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

03 Dec 2024
News

Magic Numbers

Courtesy Shalinee Sharma Courtesy Shalinee Sharma As a sixth grader in Buffalo, New York, Shalinee Sharma (MBA 2005) believed math just wasn’t her thing. There were only a few girls in the honors class at her new school, and Sharma soon realized that she was far behind... View Details

Keywords: Amy Crawford

2024
Working Paper

Fiscal Policy under Convex Supply Curves

By: Shlok Goyal, Avi Lipton and Borui Niklas Zhu

Recent empirical evidence suggests that supply curves are convex. Supply curve convexity is at odds with conventional Phillips curves, which rely on an infinitely elastic underlying supply curve. This paper explores the effect of supply curve convexity on the... View Details

Keywords: Fiscal Stimulus; Fiscal Policy; Inflation; Inflation and Deflation; Macroeconomics; Policy; Mathematical Methods; United States

2009
Working Paper

Patent Policy, Patent Pools, and the Accumulation of Claims in Sequential Innovation

By: Gaston Llanes and Stefano Trento

We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We study the equilibrium innovation activity under three regimes: patents, no-patents and patent pools. Patent pools increase the probability... View Details

Keywords: Innovation and Invention; Patents; Rights; Mathematical Methods

01 Mar 2015
News

The Next Big Swing

in 1987, the game puts players in the manager’s seat, letting them make tactical decisions against a mathematical model that determines outcomes based on everything from how a batter has historically fared against a certain pitcher to the... View Details

Keywords: Andrew Clark; Performing Arts, Spectator Sports, and Related Industries; Arts, Entertainment; Management, Scientific, and Technical Consulting Services; Professional Services; Data Processing, Hosting, and Related Services; Information

2013
Article

Where Not to Eat? Improving Public Policy by Predicting Hygiene Inspections Using Online Reviews

By: Jun Seok Kang, Polina Kuznetsova, Yejin Choi and Michael Luca

Restaurant hygiene inspections are often cited as a success story of public disclosure. Hygiene grades influence customer decisions and serve as an accountability system for restaurants. However, cities (which are responsible for inspections) have limited resources to... View Details

Keywords: Safety; Food; Governance Compliance; Mathematical Methods; Applications and Software; Public Administration Industry; Retail Industry; Food and Beverage Industry

1994
Article

Three-dimensional Finite Element Modeling of a Cervical Vertebra: An Investigation of Burst Fracture Mechanism

By: Kevin J. Bozic, J H Keyak, H B Skinner, H U Bueff and David Bradford

Finite element modeling was used to study the mechanical behavior of a cervical vertebra under axial compressive loading. A three-dimensional (3-D) finite element (FE) model of a mid-cervical vertebra using inhomogeneous material properties was generated from... View Details

Keywords: Performance Expectations; Strength and Weakness; Health; Mathematical Methods; Health Industry

January 1984
Article

A Simulation Analysis of Alternative Pricing Strategies for Dynamic Environments

By: Robert J. Dolan

Researchers of the strategic implications of the well-known demand (e.g., adoption and diffusion) and supply (e.g., experience effects) dynamics have typically sought analytical solutions. Their success in this has been achieved partly by limiting the richness of the... View Details

Keywords: Demand and Consumers; Price; Mathematical Methods; Supply and Industry

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February 2010
Supplement

Real Property Negotiation Game (CW): Excel Model

By: Arthur I. Segel, John Vogel and Justin Seth Ginsburgh

This Excel model is used to analyze the deals made in The Real Property Negotiation Game, which simulates the experience negotiating the sale, purchase, or financing of a property. View Details

Keywords: Property; Negotiation Deal; Sales; Financing and Loans; Mathematical Methods; Real Estate Industry

2009
Working Paper

Systemic Risk and the Refinancing Ratchet Effect

By: Amir E. Khandani, Andrew W. Lo and Robert C. Merton

The confluence of three trends in the U.S. residential housing market—rising home prices, declining interest rates, and near-frictionless refinancing opportunities—led to vastly increased systemic risk in the financial system. Individually, each of these trends is... View Details

Keywords: Housing; Mortgages; Risk and Uncertainty; Value; Mathematical Methods; Real Estate Industry; United States

March 2002
Article

The Potential Role of Economic Cost Models in the Regulation of Telecommunications in Developing Countries

What is the efficient cost of providing telecommunications services to a certain area or type of customer? As developing countries build up their capacity to regulate infrastructure monopolies, cost models are likely to prove increasingly important in answering... View Details

Keywords: Information; Cost; Mathematical Methods; Developing Countries and Economies; Telecommunications Industry

October 2000 (Revised March 2004)
Background Note

Variance Analysis and Flexible Budgeting

By: Robert S. Kaplan

Facilitates the teaching of cases on variance analysis and flexible budgeting. Uses algebra, diagrams, and numerical examples to illustrate the calculation of price, quantity, and mix variances for revenues and costs, and a flexible budget for analyzing indirect and... View Details

Keywords: Cost; Price; Mathematical Methods; Revenue; Budgets and Budgeting

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