Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-11T16:54:50.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Arret optimal avec contrainte

Published online by Cambridge University Press:  01 July 2016

Monique Pontier  and
Jacques Szpirglas
Monique Pontier*
Affiliation:
Université d'Orléans
Jacques Szpirglas*
Affiliation:
Centre National d'Etudes des Télécommunications
*
∗Adresse postale: Départment de Mathématiques, Université d'Orléans, 45046 Orléans-Cedex, France.
∗∗ Adresse postale: CNET/PAA/TIM/MTI. 92131 Issy les Moulineaux, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

Given two optional positive bounded processes Y and Y′, defined on a probability space , and a non-negative real a, the problem is to maximize the average reward E(YT) among all the stopping times T verifying the following constraint: The problem is solved by Lagrangian saddlepoint techniques in the set of randomized stopping times including the set of stopping times.

Keywords

OPTIMAL STOPPINGAVERAGE CONSTRAINTRANDOMIZED STOPPING TIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 798 - 812
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bibliographie

[1] Bensoussan, A. Et Lions, J. L. (1978) Applications des inéquations variationnelles en contrôle stochastique. Dunod, Paris.Google Scholar
[2] Bismut, J. M. (1974) An example of optimal control with constraints. SIAM J. Control 12, 401–418.Google Scholar
[3] Bismut, J. M. (1978) Régularité et continuité des processus. Z. Wahrscheinlichkeitsth. 44, 261–268.Google Scholar
[4] Bismut, J. M. (1979) Temps d'arrêt optimal, quasi-temps d'arrêt et retournement du temps. Ann. Prob. 7, 933–964.Google Scholar
[5] Bismut, J. M. and Skalli, B. (1977) Temps d'arrêt optimal, théorie générale des processus et processus de Markov. Z. Wahrscheinlichkeitsth. 47, 301–313.Google Scholar
[6] Christopeit, N. (1978) A stochastic control model with chance constraints. SIAM J. Control Optimization 16, 702–714.Google Scholar
[7] Dellacherie, C. (1972) Capacités et processus stochastiques. Springer-Verlag, Berlin.Google Scholar
[8] Dellacherie, C. Et Meyer, P. A. (1975), (1980) Probabilités et potentiels, Tomes 1 et 2. Hermann, Paris.Google Scholar
[9] Ekeland, I. Et Teman, R. (1976) Convex Analysis and Variational Problems. North-Holland, Amsterdam.Google Scholar
[10] El Karoui, N. (1981) Les aspects probabilistes du contrôle stochastique. Ecole d'été de St-Flour IX, 1979, Lecture Notes in Mathematics 876, Springer-Verlag, Berlin.Google Scholar
[11] Frid, E. B. (1972) On optimal strategies in control problems with constraints. Theory Prob. Appl. 17, 188–192.Google Scholar
[12] Haussmann, U. G. (1981) Some examples of optimal stochastic controls or: the stochastic maximum principle at work. SIAM Rev. 23, 292–307.Google Scholar
[13] Kennedy, D. P. (1982) On a constrained optimal stopping problem. J. Appl. Prob. 19, 631–642.Google Scholar
[14] KusHner, H. J. (1965) On the stochastic maximum principle with average constraints. J. Math. Anal. Appl. 12, 13–26.Google Scholar
[15] Mertens, J. F. (1972) Théorie des processus stochastiques généraux. Applications aux surmartingales. Z. Wahrscheinlichkeitsth. 22, 45–68.Google Scholar
[16] Neveu, J. (1972) Martingales à temps discret. Masson, Paris.Google Scholar
[17] Ozgoren, M. K., Longman, R. W. Et Cooper, C. A. (1978) Probabilistic inequality constraints in stochastic optimal control theory. J. Math. Anal. Appl. 66, 237–259.Google Scholar
[18] Quadrat, J. P. (1980) Existence de solution et algorithme de résolution numérique de problème de contrôle optimal de diffusion stochastique dégénérée ou non. SIAM J. Control Optimization 18, 199–266.Google Scholar
[19] Robin, ?. (1978) Contrôle impulsionnel de processus de Markov. Thèse, Université Paris IX.Google Scholar
[20] Robin, M. (1979) On optimal stochastic control problems with constraints. In Game Theory and Related Topics, North-Holland, Amsterdam, 187–202.Google Scholar
[21] Rockafellar, R. T. (1970) Convex Analysis. Princeton University Press, Princeton, NJ.Google Scholar
[22] Shiryayev, A. N. (1977) Optimal Stopping Rules. Applications of Mathematics 8, Springer-Verlag, Berlin.Google Scholar