Title: A utility maximisation problem on multiple time scales

Authors: Ferhan M. Atici, Daniel C. Biles, Alex Lebedinsky

Addresses: Department of Mathematics and Computer Science, Western Kentucky University, Bowling Green, KY 42101, USA. ' Department of Mathematics, Belmont University, Nashville, TN 37212, USA. ' Department of Economics, Western Kentucky University, Bowling Green, KY 42101, USA

Abstract: In this paper, we present a technique for a dynamic optimisation problem in which the value function and constraints can be on different time scales. Using this technique we solve a perfect-foresight utility maximisation problem for a finitely-lived consumer while making very general assumptions about timing of consumption and investing decisions.

Keywords: calculus of variations; time scales; delta derivative; dynamic modelling; optimisation; perfect-foresight utility maximisation; finitely-lived consumers; consumption; investment decisions; economic modelling.

DOI: 10.1504/IJDSDE.2011.038495

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.38 - 47

Published online: 09 Feb 2011 *

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