Optimal Consumption Under Deterministic Income

Julia Eisenberg (), Peter Grandits and Stefan Thonhauser
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Julia Eisenberg: Vienna University of Technology
Peter Grandits: Vienna University of Technology
Stefan Thonhauser: University of Lausanne

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 1, No 13, 255-279

Abstract: Abstract We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton–Jacobi–Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples.

Keywords: Optimal control; Optimal consumption; Value function; Hamilton–Jacobi–Bellman equation; Viscosity solutions; Semi-continuous envelopes (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-013-0320-x

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