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

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January 2008
Background Note

Index Options

By: Joshua Coval and Erik Stafford

The goal of this simulation is to understand the patterns in index option prices that are not predicted by the Black-Scholes model. In particular, the simulation focuses on two properties of options prices. First, at-the-money implied volatilities from index options... View Details

Keywords: Volatility; Stock Options; Investment; Price; Profit; Risk Management; Mathematical Methods

January 2002 (Revised October 2007)
Case

Grantham, Mayo, Van Otterloo & Co., 2001

By: Joshua Musher and Andre F. Perold

Asset manager GMO underperforms the market during the 1996-2000 stock market bubble because of the focus on absolute risk. After suffering significant client withdrawals, performance again shines when the bubble collapses. Did they win the battle only to lose the war?... View Details

Keywords: Customers; Asset Management; Stocks; Investment; Price Bubble; Mathematical Methods; Risk and Uncertainty

October 1993 (Revised August 1996)
Background Note

Forecasting with Regression Analysis

By: Arthur Schleifer Jr.

Provides an example of regression in one of its most important roles. Relating probabilistic forecasts based on past data to decision analysis. View Details

Keywords: Management Analysis, Tools, and Techniques; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods

Article

Loss Aversion, Diminishing Sensitivity, and the Role of Experience in Repeated Decisions

Three experiments are presented that explore the assertion that loss aversion and diminishing sensitivity drive the effect of experience on choice behavior. The experiments are focused on repeated choice tasks where decision makers choose repeatedly between... View Details

Keywords: Experience and Expertise; Decision Choices and Conditions; Mathematical Methods; Loss

February 2005 (Revised November 2016)
Background Note

Forecasting the Adoption of a New Product

Provides tools and methodologies that allow forecasting demand for innovative new products. Highlights the Bass model—the theory behind it and ways to determine its parameters. Provides a detailed example of how to use the Bass model to forecast demand for satellite... View Details

Keywords: Forecasting and Prediction; Innovation and Invention; Marketing; Demand and Consumers; Mathematical Methods; Competition

January 2003 (Revised January 2008)
Case

The British Motorcycle Industry at a Crossroads

By: Jan W. Rivkin

By 1975, the collapse of the British motorcycle industry is nearly complete. Only one British manufacturer, NVT, remains in operation. In this setting, the British government commissions the Boston Consulting Group to identify and evaluate strategic alternatives for... View Details

Keywords: Cost; Industry Structures; Business and Government Relations; Mathematical Methods; Competition; Consulting Industry; Manufacturing Industry; Motorcycle Industry; Great Britain

March 2022
Article

Where to Locate COVID-19 Mass Vaccination Facilities?

By: Dimitris Bertsimas, Vassilis Digalakis Jr, Alexander Jacquillat, Michael Lingzhi Li and Alessandro Previero

The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new... View Details

Keywords: Vaccines; COVID-19; Health Care and Treatment; Health Pandemics; Performance Effectiveness; Analytics and Data Science; Mathematical Methods

2007
Working Paper

Recognizing the New: A Multi-Agent Model of Analogy in Strategic Decision-Making

By: Giovanni Gavetti and Massimo Warglien

In novel environments, strategic decision-making is often premised on analogy, and recognition lies at its heart. Recognition refers to a class of cognitive processes through which a problem is interpreted associatively in terms of something that has been experienced... View Details

Keywords: Interpersonal Communication; Decision Choices and Conditions; Mathematical Methods; Cognition and Thinking; Power and Influence

July 1996 (Revised June 2001)
Case

Atlantic Corporation-Abridged

By: Thomas R. Piper

A major paper company is considering acquiring the assets of a company that is threatened by a hostile takeover. The acquisition can be evaluated in terms of industry attractiveness, comparative advantage, and cash-flow analysis. View Details

Keywords: Projects; Cash Flow; Interest Rates; Valuation; Mathematical Methods; Horizontal Integration; Acquisition; Competitive Advantage; Aerospace Industry

November 1999 (Revised June 2001)
Case

Seitel, Inc.

By: David F. Hawkins

The company's accounting for its seismic data library is questioned. Teaching Purpose: Inventory accounting. View Details

Keywords: Stock Shares; Financial Statements; Business Earnings; Financial Reporting; Stock Options; Mathematical Methods; Accounting Industry

November 1992
Case

Process Control at Polaroid (B)

By: H. Kent Bowen and Steven C. Wheelwright

The plant manager of a film production operation wants to create and implement a new approach to quality within the next 12 months. Issues of personnel (and their roles), production processes (and their control), and quality standards must be addressed. View Details

Keywords: Employee Relationship Management; Job Design and Levels; Management Practices and Processes; Production; Quality; Mathematical Methods

May 2009 (Revised December 2009)
Teaching Note

Reliance Baking Soda: Optimizing Promotional Spending (Brief Case)

By: John A. Quelch and Heather Beckham

Teaching Note to Briefcase 4128 View Details

Keywords: Quantitative Analysis; Consumer Marketing; Marketing Planning; Product Management; Sales Promotions; Program Budgeting; Marketing Strategy; Marketing Channels; Mathematical Methods; Advertising; Budgets and Budgeting; Product Marketing; Communication Strategy

2010
Chapter

Facts and Fallacies about U.S. FDI in China

By: Lee Branstetter and C. Fritz Foley

Despite the rapid expansion of U.S.-China trade ties, the increase in U.S. FDI in China, and the expanding amount of economic research exploring these developments, a number of misconceptions distort the popular understanding of U.S. multinationals in China. In this... View Details

Keywords: Expansion; Trade; Foreign Direct Investment; Mathematical Methods; Multinational Firms and Management; China; United States

2007
Working Paper

Optimal Reserve Management and Sovereign Debt

By: Laura Alfaro and Fabio Kanczuk

Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign's willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming... View Details

Keywords: Sovereign Finance; Borrowing and Debt; Financial Liquidity; International Finance; Emerging Markets; Mathematical Methods

Fourth Quarter 2007
Article

Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk

By: Dale . F. Gray, Robert C. Merton and Zvi Bodie

This paper proposes a new approach to measure, analyze, and manage sovereign risk based on the theory and practice of modern contingent claims analysis (CCA). The paper provides a new framework for adapting the CCA model to the sovereign balance sheet in a way that can... View Details

Keywords: Credit; Investment; Sovereign Finance; Risk Management; Emerging Markets; Market Transactions; Mathematical Methods; Valuation

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April 2011
Teaching Note

Neck & Neck: Leveraging the Club Neck Information (TN)

Teaching Note for 111112. View Details

Keywords: Budgets and Budgeting; Knowledge Use and Leverage; Profit; Planning; Advertising Campaigns; Mathematical Methods; Apparel and Accessories Industry; Retail Industry

June 2011 (Revised January 2013)
Case

Oddo Securities―ESG Integration

By: Paul M. Healy

The case describes the process of integrating environmental, social, and governance issues into valuation models and research analyst recommendations. View Details

Keywords: Financial Strategy; Mathematical Methods; Integration; Valuation; Environmental Sustainability; Social Issues; Governance Controls; Investment

November 2006
Background Note

Technical Game Theory Note #1: Solving Bi-matrix Games

By: Dennis A. Yao

Explains how to solve bi-matrix games and introduces the Nash Equilibrium concept. View Details

Keywords: Game Theory; Mathematical Methods; Learning; Balance and Stability; Planning; Strategic Planning; Performance Improvement; Strategy; Games, Gaming, and Gambling

January 2010 (Revised October 2011)
Case

The Congressional Oversight Panel's Valuation of the TARP Warrants (A)

By: Carliss Y. Baldwin

The Congressional Oversight Panel wants to value the warrants issued to the government in connection with the TARP investments of 2008, in order to increase the transparency of options repurchases. The case describes the methodology used to value the warrants. Students... View Details

Keywords: Financial Crisis; Asset Pricing; Financial Instruments; Investment; Business and Government Relations; Mathematical Methods; Valuation; Banking Industry; Public Administration Industry; United States

December 2012
Case

Delwarca Software Remote Support Unit

By: Roy D. Shapiro and Paul E. Morrison

Delwarca Software provides business software to large corporate clients around the world. The firm serves customers who prefer to assemble corporate solutions using a combination of software programs from various suppliers rather than implementing a single enterprise... View Details

Keywords: Service Operations; Service Delivery; Mathematical Methods; Applications and Software; Problems and Challenges; Customer Satisfaction; Information Technology Industry

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