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On the dynamic programming inequalities associated with the deterministic optimal stopping problem in discrete and continuous time. (English) Zbl 0476.49021

MSC:
49L20 Dynamic programming in optimal control and differential games
49J40 Variational inequalities
60G40 Stopping times; optimal stopping problems; gambling theory
90C39 Dynamic programming
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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References:
[1] Bardos C., Ann. Scient. Ec. Norm. Sup. pp 185– (1970)
[2] Bensoussan A., Cahièrs du Ceremade (1980)
[3] Bensoussan, A. ”Stochastic control by functional analysis methods”. to appear · Zbl 0474.93002
[4] Bensoussan, A. and Lions, J.L. 1978. ”Applications des Inèquations Variationnelles en Controle Stochastique”. Paris: Dunod. · Zbl 0411.49002
[5] Bensoussan A., On the convergence of the discrete time dynamic programming equation for general semigroups · Zbl 0488.93062 · doi:10.1137/0320053
[6] Capuzzo Dolcetta I., A constructi- ve approach to the deterministic stopping time problem · Zbl 0492.49013
[7] Henrici, P. 1962. ”Discrete variable methods in ordinary differential equations”. N.Y.: John Wiley. · Zbl 0112.34901
[8] Menaldi J.L., Le probleme de temps d’arret optimal deterministe et l’inequation variationnelle du I ordre associee
[9] Zabczyk, J. ”Semigroup methods in stochastic control theory”. Univ. de Montreal. CRM-821 · Zbl 0567.93076
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