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Optimal control of a commercial loan repayment plan

Pages: 345 - 354, Issue Special, August 2005

 Abstract        Full Text (124.4K)              

Ellina Grigorieva - Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204, United States (email)
Evgenii Khailov - Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russian Federation (email)

Abstract: We consider a controlled system of differential equations modeling a firm that takes a loan in order to expand its production activities. The objective is to determine the optimal loan repayment schedule using the variables of the business current profitability, the bank's interest rate on the loan and the cost of reinvestment of capital. The portion of the annual profit which a firm returns to the bank and the value of the total loan taken by the firm are control parameters. We consider a linear production function and investigate the attainable sets for the system analytically and numerically. Optimal control problems are stated and their solutions are found using attainable sets. Attainable sets for different values of the parameters of the system are constructed with the use of a computer program written in MAPLE. Possible economic applications are discussed.

Keywords:  Controlled system, attainable set, microeconomic dynamical model.
Mathematics Subject Classification:  49J15, 58E25, 90A16, 93B03.

Received: September 2004;      Revised: March 2005;      Published: September 2005.