Annals of Operations Research

, Volume 205, Issue 1, pp 29-53

First online:

A dynamic theory of the credit union

  • Geoffrey M. RubinAffiliated withCanada Pension Plan Investment Board
  • , George A. OverstreetJr.Affiliated withMcIntire School of Commerce, University of Virginia
  • , Peter BelingAffiliated withDepartment of Systems and Information Engineering, University of Virginia
  • , Kanshukan RajaratnamAffiliated withDepartment of Finance & Tax and the African Collaboration for Quantitative Finance & Risk Research (ACQuFRR), University of Cape Town Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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