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      Mathematical MethodsRemove Mathematical Methods →

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      • 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
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      Alfaro, Laura, and Fabio Kanczuk. "Optimal Reserve Management and Sovereign Debt." NBER Working Paper Series, No. 13216, July 2007.
      • June 2007
      • Article

      Which Levers Boost ROI?

      By: Margeaux Cvar and John A. Quelch
      The article refers to ROI, or return on investment, and focuses on a rational strategy for financial markets that uses outside industry comparisons. The first step is to identify parallel businesses that have similar characteristics such as growth, capital, and market... View Details
      Keywords: Mathematical Methods; Financial Markets; Investment Return
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      Cvar, Margeaux, and John A. Quelch. "Which Levers Boost ROI?" Harvard Business Review 85, no. 6 (June 2007): 21–24.
      • February 2007 (Revised January 2008)
      • Supplement

      Multifactor Models (CW)

      By: Malcolm P. Baker
      Keywords: Asset Pricing; Cost of Capital; Forecasting and Prediction; Investment Funds; Investment Return; Mathematical Methods; Performance Evaluation
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      Baker, Malcolm P. "Multifactor Models (CW)." Harvard Business School Spreadsheet Supplement 207-710, February 2007. (Revised January 2008.)
      • November 2006
      • Background Note

      Technical Game Theory Note #6: Multiple-Round Games and Reputations

      By: Dennis A. Yao
      Provides a game theory-based interpretation of reputations and reputation building. View Details
      Keywords: Game Theory; Mathematical Methods; Games, Gaming, and Gambling; Reputation; Debates; Strategy; Performance Consistency; Performance Improvement; Strategic Planning; Education Industry
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      Yao, Dennis A. "Technical Game Theory Note #6: Multiple-Round Games and Reputations." Harvard Business School Background Note 707-488, November 2006.
      • November 2006
      • Case

      Introducing Frequent Flyer Programs

      By: Dennis A. Yao
      Allows students to explore the value to American Airlines of introducing a frequent flyer program in 1981. View Details
      Keywords: Value; Management Analysis, Tools, and Techniques; Mathematical Methods; Game Theory; Competitive Advantage; Programs; Customers; Air Transportation Industry
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      Yao, Dennis A. "Introducing Frequent Flyer Programs." Harvard Business School Case 707-479, November 2006.
      • 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
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      Yao, Dennis A. "Technical Game Theory Note #1: Solving Bi-matrix Games." Harvard Business School Background Note 707-476, November 2006.
      • 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).
      • 2006
      • Chapter

      A Decision Perspective on Organizations: Social Cognition, Behavioral Decision Theory and the Psychological Links to Micro and Macro Organizational Behaviour

      By: M. A. Neale, A. E. Tenbrunsel, T. Galvin and M. H. Bazerman
      Keywords: Decision Making; Perspective; Behavior; Cognition and Thinking; Organizations; Mathematical Methods
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      Neale, M. A., A. E. Tenbrunsel, T. Galvin, and M. H. Bazerman. "A Decision Perspective on Organizations: Social Cognition, Behavioral Decision Theory and the Psychological Links to Micro and Macro Organizational Behaviour." In The SAGE Handbook of Organization Studies. 2nd ed. Edited by Stewart R. Clegg, Cynthia Hardy, Thomas Lawrence, and Walter Nord. Sage Publications, 2006.
      • July 2006
      • Article

      Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows

      By: Ramon Casadesus-Masanell and Pankaj Ghemawat
      This paper analyzes a dynamic mixed duopoly in which a profit-maximizing competitor interacts with a competitor that prices at zero (or marginal cost), with the cumulation of output affecting their relative positions over time. The modeling effort is motivated by... View Details
      Keywords: Open Source Software; Demand-side Learning; Network Effects; Linux; Mixed Duopoly; Competitive Dynamics; Business Models; Duopoly and Oligopoly; Information Technology; Applications and Software; Business Model; Mathematical Methods; Digital Platforms; Profit; Balance and Stability; Management Analysis, Tools, and Techniques; SWOT Analysis; Competition; Price; Information Technology Industry
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      Casadesus-Masanell, Ramon, and Pankaj Ghemawat. "Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows." Management Science 52, no. 7 (July 2006): 1072–1084.
      • June 2006 (Revised March 2007)
      • Teaching Note

      Polyphonic HMI: Mixing Music and Math

      By: Anita Elberse
      Keywords: Mathematical Methods; Music Industry
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      Elberse, Anita. "Polyphonic HMI: Mixing Music and Math." Harvard Business School Teaching Note 506-081, June 2006. (Revised March 2007.)
      • 2006
      • Chapter

      Advanced Regression Models

      By: Raghuram Iyengar and Sunil Gupta
      Keywords: Mathematical Methods
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      Iyengar, Raghuram, and Sunil Gupta. "Advanced Regression Models." In Handbook of Marketing Research, edited by Rajiv Grover. Sage Publications, 2006.
      • 2006
      • Chapter

      Interorganizational Cooperation between Not-for-profit Organizations: A Relational Analysis

      By: Julie Battilana and Metin Sengul
      Keywords: Nonprofit Organizations; Cooperation; Mathematical Methods
      Citation
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      Battilana, Julie, and Metin Sengul. "Interorganizational Cooperation between Not-for-profit Organizations: A Relational Analysis." In Relational Perspectives in Organization Studies: A Research Companion, edited by Olympia Kyriakidou and Mustafa F. Özbilgin, 197–220. Cheltenham, U.K.: Edward Elgar Publishing, 2006.
      • April 2006
      • Background Note

      Informing Service Management with Customer Data

      By: Frances X. Frei and Dennis Campbell
      Taught as the third module in a Harvard Business School course on Managing Service Operations. Explores the role of data analysis in ongoing service management. Describes how to realize the maximum amount of value from analyses and use this information in... View Details
      Keywords: Decision Making; Design; Analytics and Data Science; Service Operations; Mathematical Methods; Value
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      Frei, Frances X., and Dennis Campbell. "Informing Service Management with Customer Data." Harvard Business School Background Note 606-097, April 2006.
      • February 2006
      • Teaching Note

      Cost-Volume-Profit Models (TN)

      By: David F. Hawkins, V.G. Narayanan, Michele Jurgens and Jacob Cohen
      Keywords: Mathematical Methods
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      Hawkins, David F., V.G. Narayanan, Michele Jurgens, and Jacob Cohen. "Cost-Volume-Profit Models (TN)." Harvard Business School Teaching Note 106-046, February 2006.
      • January 2006
      • Tutorial

      Cost-Volume Profit Models

      By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
      Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
      Keywords: Volume; Cost; Profit; Mathematical Methods
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      "Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
      • 2006
      • Working Paper

      On the Origin of Shared Beliefs (and Corporate Culture)

      By: Eric J. Van den Steen

      This paper shows why members of an organization often share similar beliefs. I argue that there are two mechanisms. First, when performance depends on making correct decisions, people prefer to work with others who share their beliefs and assumptions, since such... View Details

      Keywords: Organizational Culture; Employees; Values and Beliefs; Mathematical Methods
      Citation
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      Van den Steen, Eric J. "On the Origin of Shared Beliefs (and Corporate Culture)." Sloan School of Management Working Paper, No. 4553-05, January 2006. (Available at SSRN.)
      • December 2005 (Revised March 2007)
      • Case

      Innovation and Collaboration at Merrill Lynch

      By: Boris Groysberg and Ingrid Vargas
      In the spring of 2005, Candace Browning, head of Global Securities Research and Economics at Merrill Lynch, led about 500 Merrill Lynch analysts worldwide in a collaborative effort to produce innovative research, most of them accustomed to working independently in... View Details
      Keywords: Leadership; Groups and Teams; Management Teams; Decision Making; Collaborative Innovation and Invention; Negotiation; Mathematical Methods; Strategy; Human Resources; Motivation and Incentives; Banking Industry; Financial Services Industry
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      Groysberg, Boris, and Ingrid Vargas. "Innovation and Collaboration at Merrill Lynch." Harvard Business School Case 406-081, December 2005. (Revised March 2007.)
      • October 2005 (Revised February 2010)
      • Background Note

      Calculating Free Cash Flows

      By: Robin Greenwood and David S. Scharfstein
      Outlines the mechanics of calculating free cash flows from historical and proforma financial statements. Focuses on the mechanical process of transforming numbers from financial forecasts into cash flows. View Details
      Keywords: Financial Statements; Forecasting and Prediction; Cash Flow; Mathematical Methods
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      Greenwood, Robin, and David S. Scharfstein. "Calculating Free Cash Flows." Harvard Business School Background Note 206-028, October 2005. (Revised February 2010.)
      • 2005
      • Chapter

      A Revised Model of the Resource Allocation Process

      By: J. L. Bower and Clark Gilbert
      Keywords: Resource Allocation; Mathematical Methods
      Citation
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      Bower, J. L., and Clark Gilbert. "A Revised Model of the Resource Allocation Process." In From Resource Allocation to Strategy, edited by Joseph L. Bower and Clark Gilbert. U.K.: Oxford University Press, 2005.
      • August 2005 (Revised April 2008)
      • Teaching Note

      GuestFirst Hotel (A): Statistics Review with Data Desk (TN)

      By: Frances X. Frei
      Presents an overview of the statistical analysis covered in the case discussion. View Details
      Keywords: Mathematical Methods
      Citation
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      Frei, Frances X. "GuestFirst Hotel (A): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-038, August 2005. (Revised April 2008.)
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