Publications

2020
Working Paper

Demystifying the Math of the Coronavirus

By: Elon Kohlberg and Abraham Neyman

We provide an elementary mathematical description of the spread of the coronavirus. We explain two fundamental relationships: How the rate of growth in new infections is determined by the “effective reproductive number” and how the effective reproductive number is... View Details

Keywords: Coronavirus; Health Pandemics; Mathematical Methods

Article

Improved Bounds on the Sizes of S.P Numbers

By: Paul Myer Kominers and Scott Duke Kominers

A number which is S.P in base r is a positive integer which is equal to the sum of its base-r digits multiplied by the product of its base-r digits. These numbers have been studied extensively in The Mathematical Gazette. Recently, Shah Ali... View Details

Keywords: Mathematical Methods

August 2001
Technical Note

Technical Note on Expectations

By: Carliss Y. Baldwin

Reviews the mathematics of expectations embedded in a company's current stock price and the related (whole) enterprise value. Begins by showing how the current stock price can be compounded forward to arrive at an expectation one or more years in the future. Describes... View Details

Keywords: Performance Expectations; Price; Stocks

Research Summary

An Impossibility Theorem on Beliefs in Games (with H. Jerome Keisler)

A 'paradox' of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to (a weak form of) Tarski's Theorem of mathematical logic. A rough interpretation of the theorem is that if a model of a game is available to the... View Details

December 2019
Technical Note

Technical Note on Bayesian Statistics and Frequentist Power Calculations

By: Amitabh Chandra and Ariel Dora Stern

This Technical Note provides an introduction to Bayes’ Rule and the statistical intuition that stems from it. In this note, we review the concepts that underlie Bayesian statistics, and we offer several simple mathematical examples to illustrate applications of Bayes’... View Details

Keywords: Bayesian Statistics; Mathematical Methods

July–August 2011
Article

Robust Optimization Made Easy with ROME

By: Joel Goh and Melvyn Sim

We introduce ROME, an algebraic modeling toolbox for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically... View Details

Keywords: Robust Optimization; Algebraic Modeling Toolbox; MATLAB; Stochastic Programming; Decision Rules; Inventory Control; PERT; Project Management; Portfolio Optimization; Information Technology; Mathematical Methods; Operations

June 2013 (Revised November 2022)
Exercise

Competition Simulator Exercise

By: Eric J. Van den Steen

In the Competition Simulator Exercise, students explore through trial and error some important economic foundations of competitive strategy and managerial economics. In particular, the nine simulator exercises let students explore horizontal differentiation with and... View Details

Keywords: Competition; Economics; Game Theory; Competitive Strategy; Learning; Mathematical Methods; Analysis

Research Summary

Game Theory for Business Strategy

Game theory--the mathematical study of strategic interactions--came of age, in a sense, when three of the field's pioneers were awarded the Nobel Prize in Economics in 1994. Yet despite the development of the theory and the widespread use of game-theoretic jargon in... View Details

Article

Matriarch: A Python Library for Materials Architecture

By: Tristan Giesa, Ravi Jagadeesan, David I. Spivak and Markus J. Buehler

Biological materials, such as proteins, often have a hierarchical structure ranging from basic building blocks at the nanoscale (e.g., amino acids) to assembled structures at the macroscale (e.g., fibers). Current software for materials engineering allows the user to... View Details

Keywords: Building Block; Category Theory; Hierarchical Protein Materials; Molecular Design; Open-Source Software; Structure Creation

Research Summary

Valuation Theory and Practice

Timothy A. Luehrman's primary research interest is in the application of valuation methods to companies, businesses, and individual assets. Some of his work involves applications of tools originally developed for valuing derivative securities to the valuation of other... View Details

Article

Risk and the Cross-Section of Stock Returns

By: Mark Seasholes, Radu Burlacu, Patrice Fontaine and Sonia Jimenez-Garces

This paper mathematically transforms unobservable rational expectation equilibrium model parameters (information precision and supply uncertainty) into a single variable that is correlated with expected returns and that can be estimated with recently observed data. Our... View Details

Keywords: Risk Premiums; Cross-sectional Asset Pricing; REE Models; Risk and Uncertainty; Asset Pricing; Investment Return

June 2012 (Revised July 2013)
Exercise

Competition Simulator Exercise: Instructions

By: Eric Van den Steen

Keywords: Competitive Strategy; Economics; Strategy; Game Theory

Research Summary

Overview

Professor Goh’s primary research interest is applying mathematical models to real-world problems in health care in order to inform, improve, and enhance medical decision making and health policy. His recent work in this domain focuses on developing new methods for... View Details

Keywords: Uncertainty; Optimization; Inventory Management; Health; Decision Making; Supply Chain

2021
Conference Presentation

An Algorithmic Framework for Fairness Elicitation

By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu

We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details

Keywords: Algorithmic Fairness; Machine Learning; Fairness; Framework; Mathematical Methods

November 2007
Background Note

Asset Allocation I

By: Joshua D. Coval, Erik Stafford, Rodrigo Osmo, John Jernigan, Zack Page and Paulo Passoni

The goal of these simulations is to understand the mathematics of mean-variance optimization and the equilibrium pricing of risk if all investors use this rule with common information sets. Simulation A focuses on five to 10 years of monthly sector returns that are... View Details

Keywords: Asset Pricing; Capital; Investment Return; Risk Management; Mathematical Methods

April 2020 (Revised October 2022)
Case

Medellín Reborn (A)

By: Jorge Tamayo, Ashish Nanda and Margaret Cross

In 2003, mathematics professor Sergio Fajardo was elected mayor of Medellín, Colombia—one of the most violent cities in the world at that time. As mayor, Fajardo faced a host of daunting challenges. Rampant gang violence had raised Medellín’s homicide rate... View Details

Keywords: Strategic Leadership; Peace; Government; Politics; Priorities; Leadership; City; Strategy; Government and Politics; Problems and Challenges; Transformation; Government Administration; Crime and Corruption; Colombia; Medellín

July 2023 (Revised July 2023)
Background Note

Generative AI Value Chain

By: Andy Wu and Matt Higgins

Generative AI refers to a type of artificial intelligence (AI) that can create new content (e.g., text, image, or audio) in response to a prompt from a user. ChatGPT, Bard, and Claude are examples of text generating AIs, and DALL-E, Midjourney, and Stable Diffusion are... View Details

Keywords: AI; Artificial Intelligence; Model; Hardware; Data Centers; AI and Machine Learning; Applications and Software; Analytics and Data Science; Value