Optimal consumption under deterministic income

Julia Eisenberg*, Peter Grandits, Stefan Michael Thonhauser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)255-279
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 2014

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