Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin
On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin
Mathematics Faculty Research Publications
The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact.
On Some Ergodic Impulse Control Problems With Constraint, J. L. Menaldi, Maurice Robin
On Some Ergodic Impulse Control Problems With Constraint, J. L. Menaldi, Maurice Robin
Mathematics Faculty Research Publications
This paper studies the impulse control of a general Markov process under the average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous process, and this restriction is referred to as a constraint. A detailed setting is described, a characterization of the optimal cost is obtained as a solution of an HJB equation, and an optimal impulse control is identified.
On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin
On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.
On Some Optimal Stopping Problems With Constraint, J. L. Menaldi, M. Robin
On Some Optimal Stopping Problems With Constraint, J. L. Menaldi, M. Robin
Mathematics Faculty Research Publications
We consider the optimal stopping problem of a Markov process {xt : t ≤ 0} when the controller is allowed to stop only at the arrival times of a signal, that is, at a sequence of instants {τn : n ≤ 1} independent of {xt : t ≤ 0}. We solve in detail this problem for general Markov–Feller processes with compact state space when the interarrival times of the signal are independent identically distributed random variables. In addition, we discuss several extensions to other signals and to other cases of state spaces. These results …