Annals of Operations Research

, Volume 205, Issue 1, pp 29–53 | Cite as

A dynamic theory of the credit union

  • Geoffrey M. Rubin
  • George A. OverstreetJr.
  • Peter Beling
  • Kanshukan Rajaratnam


A topic of recent interest in the retail financial sector has been the growth of credit unions or “pure cooperatives”. Past credit union researchers built mathematical models of credit union operations. These models identified important operating characteristics but were modeled under assumptions of static operating environments. The model presented in this paper departs from the traditional static models and examines dynamic operation for a United States credit union. Its inter-temporal structure clarifies a number of issues—such as optimal equity retention and inter-temporal rate policy—not addressed by earlier studies. Given initial conditions, the model specifies equity retention and inter-temporal deposit and loan rate policies until an equilibrium state is reached.


Credit union Optimal control Capital management Financial services 



The authors are grateful to the anonymous reviewers, who provided many helpful comments and suggestions for improvement. Funding of this research work was, in part, supported by the University of Cape Town Research Office and the Carnegie Research Development Grant.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Geoffrey M. Rubin
    • 1
  • George A. OverstreetJr.
    • 2
  • Peter Beling
    • 3
  • Kanshukan Rajaratnam
    • 4
  1. 1.Canada Pension Plan Investment BoardTorontoCanada
  2. 2.McIntire School of CommerceUniversity of VirginiaCharlottesvilleUSA
  3. 3.Department of Systems and Information EngineeringUniversity of VirginiaCharlottesvilleUSA
  4. 4.Department of Finance & Tax and the African Collaboration for Quantitative Finance & Risk Research (ACQuFRR)University of Cape TownRondeboschSouth Africa

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