Maximum principle for control problems with uncertain horizon and variable discount rate
- 74 Downloads
We consider an optimal control problem in which the time horizon is a random variable and the discount factor may depend on the past state and control values. This problem combines features of controlled piecewise deterministic processes and recursive utility maximization. Applying a simple transformation and a refined version of Halkin's proof of the maximum principle for optimal control problems on unbounded time intervals (Ref. 1), we obtain the maximum principle for the problem under consideration. Our assumptions are weaker than those of related results in the literature.
Key WordsOptimal control maximum principle piecewise deterministic processes recursive utility maximization
Unable to display preview. Download preview PDF.
- 1.Halkin, H.,Necessary Conditions for Optimal Control Problems with Infinite Horizons, Econometrica, Vol. 42, pp. 267–272, 1974.Google Scholar
- 2.Vermes, D.,Optimal Control of Piecewise Deterministic Markov Process, Stochastics, Vol. 14, pp. 165–208, 1985.Google Scholar
- 3.Boukas, E. K., Haurie, A., andMichel, P.,An Optimal Control Problem with a Random Stopping Time, Journal of Optimization Theory and Applications, Vol. 64, pp. 471–480, 1990.Google Scholar
- 4.Michel, P.,On the Transversality Condition in Infinite-Horizon Optimal Control Problems, Econometrica, Vol. 50, pp. 975–985, 1982.Google Scholar
- 5.Koopmans, T. C.,Stationary Ordinal Utility and Impatience, Econometrica, Vol. 28, pp. 287–309, 1960.Google Scholar
- 6.Becker, R. A., Boyd, J. H., III, andSung, B. Y.,Recursive Utility and Optimal Capital Accumulation, Part 1: Existence, Journal of Economic Theory, Vol. 47, pp. 76–100, 1989.Google Scholar
- 7.Becker, R. A., andBoyd, J. H., III,Recursive Utility and Optimal Capital Accumulation, Part 2: Sensitivity and Duality Theory, Mimeo, Indiana University, Bloomington, Indiana, 1989.Google Scholar
- 8.Stern, L. E.,Criteria of Optimality in the Infinite-Time Optimal Control Problem, Journal of Optimization Theory and Applications, Vol. 44, pp. 497–508, 1984.Google Scholar