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Our Resource Center provides case studies, technical papers, academic papers, and books among other resources to demonstrate the application and benefits of our solutions. We also provide information on the practical use and theory behind recursive methods. We will continue to update this page with our latest studies and findings, so check back often.

Case Studies

Optimizing Promotional Strategy with Rapid Recursive®

This case study demonstrates the capabilities of our Marketing & Promotional Strategy solutions by applying them to a large, publicly available dataset of charitable donors. This particular organization had a history of successful mail campaigns, however, they had an opportunity to improve. Read this case study to see how we were able to predict customer responses to within 3% over a 12 month period. Our strategy suggestion would have improved profits by 30%.


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Valuation of a High Risk Startup with Rapid Recursive®

This case study is currently under development and will be posted here soon.


Technical Papers

The Value of a Controlling Interest in an Expropriated Oil & Gas Company: YPF SA
Patrick Anderson, Mar 2013

This paper demonstrates the application and benefits of recursive methods for financial valuation. The objective is to value the controlling interest Repsol (Spanish firm) held in the integrated oil and gas corporation, YPF Sociedad Anonima, until its expropriation by the Argentine national government in May 2012.


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Microeconomic Applications of the Rapid Recursive® Toolbox
Jeffrey Johnson, Apr 2013


This technical paper demonstrates the practical application of the Rapid Recursive® Toolbox to five classical sequential decision problems in Economics.


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Optimal Search for a Moving Target with Two-Way Path Constraints
Jeffrey Johnson, Apr 2013


This technical paper presents an application of a novel recursive method, using the Rapid Recursive® Toolbox, to quickly determine an optimal path in the search for a moving target.


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Valuing Rental Properties Using a Recursive Model
David Quach, Mar 2013

Example Decision Process: Rental Property Owner

This technical paper presents a recursive method approach to valuing rental properties. The recursive method is used to calculate the value of an actual rental property in the state of Michigan in the United States. Data used in the valuation model is provided by the property’s owner.


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A Basic Job Search Model
David Quach, Mar 2013

This technical paper presents a basic model of conducting a job search. The model is analyzed to demonstrate the reservation wage property, where a worker will accept any wage offer above the reservation wage and will reject all other offers. The model is then solved numerically using the Rapid Recursive® Toolbox.


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Journal Articles

Persistent Unemployment & Policy Uncertainty:

Numerical Evidence from a New Approach

Patrick Anderson, our executive chairman, used the Rapid Recursive® Toolbox for his paper “Persistent Unemployment & Policy Uncertainty,” published in the January 2014 edition of Business Economics. Patrick won the 2013 Edmund A. Mennis award from the National Association of Business Economics (NABE) for this paper.
In the recovery from the United States’ 2009 recession, unemployment has proven resistant to both aggressive fiscal policy and expansionary monetary policy. A possible explanation is the policy cost uncertainty hypothesis. For this, Patrick used a novel “value functional” or “recursive” model of firm behavior, in which managers maximize the value of the business rather than its profits. Using this approach, he demonstrated that policy cost uncertainty affects the hiring decisions of firms, that the response to policy uncertainty is higher in some industries than others, and that the scale of the firm also affects its sensitivity to policy risk.


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Other Resources

Intellectual History of Recursive Methods

Recursive methods have been developed and written about by award-winning scholars in the fields of economics, finance, and statistics (control theory) since the 1950s. In an effort to provide additional insight, we have provided information on, and links to major works discussing recursive methods. Our collection includes the Guide to Recursive Models that introduces important concepts, and other information on how to create a recursive model.


Richard Bellman pioneers a recursive method of solving multi-period decision problems under uncertainty in his book Dynamic Programming. He noted at that time the severe difficulties in using the method, including the “curse of dimensionality.” The American Automatic Control Council established the Richard E. Bellman Control Heritage Award in 1979. This award is given annually for “achievements in Control Theory.”


Recursive Methods in Economic Dynamics Cover

Nancy Stokey and Robert Lucas establish important existence properties and other mathematical underpinnings of recursive methods in book Recursive Methods in Economic Dynamics (Harvard University Press, 1989). The book becomes a seminal work for next generation of economists. Robert Lucas was the recipient of the 1995 Nobel Prize in Economics.


Investment Under Uncertainty

Avinash Dixit and Robert Pindyck describe the failings of traditional methods to solve common investment and business management problems in their book Investment Under Uncertainty (Princeton University Press, 1994). They demonstrated the theoretical superiority of a recursive model to some of these same problems.



Recursive Macroeconomic Theory Cover

Lars Lungqvist and Thomas Sargent outline multiple recursive models in the field of theoretical economics in Recursive Macroeconomic Theory (MIT Press, 2000), and revise the text in two additional editions. It becomes a standard text for advanced Economics students. Thomas Sargent was the recipient of the 2011 Nobel Prize n Economics.



Patrick Anderson outlines the direct application of recursive methods to numerous business management and life decision problems. He also provides the theoretical bases for such applications, and composes and solves examples in the book using a prototype of the toolbox. Read about Patrick Anderson’s award in the section above.


The Guide to Recursive Models

By Patrick Anderson

Our Guide to Recursive Models introduces concepts of sequential decision problems, and the recursive approach to solving such problems. The guide also presents a rich set of models that represent common decision problems. These models can be immediately solved by the Rapid Recursive® Toolbox.


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The Solutions Manual and Reference for The Economics of Business Valuation

By Erin Grover

Our Solutions Manual and Reference for the Economics of Business Valuation is a supplemental reference to Economics of Business Valuation and provides a rich set of examples created by the Rapid Recursive® Toolbox.


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As we make new discoveries and create solutions for our customers, we will add additional resources to this page. Please visit the Rapid Recursive® Toolbox page and Rapid Recursive® Method page for more information on our software and methods.