On some cheap control problems for diffusion processes

Menaldi, José Luis; Robin, Maurice

doi:10.1090/s0002-9947-1983-0701523-2

Cited by 59 publications

(25 citation statements)

References 14 publications

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“…The decision makers are allowed to choose a sequence of stopping times (intervention times) {τ 1 , τ 2 , · · · }, and a sequence of impulses controls {ζ 1 , ζ 2 , · · ·} to be imposed upon the system at {τ 1 , τ 2 , · · · } respectively; e.g. [4], [10], [15], [16]. Explicit solutions are possible for simple cases with infinite time horizon.…”

Section: Assumptionmentioning

confidence: 99%

Some control problems with random intervention times

Wang

2001

Advances in Applied Probability

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We consider the problem of optimally tracking a Brownian motion by a sequence of impulse controls, in such a way to minimize the total expected cost that consists of a quadratic deviation cost and a proportional control cost. The main feature of our model is that the control can only be exerted at the arrival times of an exogenous uncontrolled Poisson process (signal). In other words, the set of possible intervention times are discrete, random and determined by the signal process (not by the decision maker). We discuss both the discounted problem and the ergodic problem, where explicit solutions can be found. We also derive the asymptotic behavior of the optimal control policies and the value functions as the intensity of the Poisson process goes to infinity, or roughly speaking, as the set of admissible controls goes from the discrete-time impulse control to the continuous-time bounded variation control.

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Section: Assumptionmentioning

confidence: 99%

Some control problems with random intervention times

Wang

2001

Advances in Applied Probability

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“…which implies (39). Finally, the strict positivity of A follows from (17) and the inequality in (38).…”

Section: Thus We Have Proved That V(x Y) ≤ W(x Y)mentioning

confidence: 81%

Irreversible Capital Accumulation with Economic Impact

Motairi

Zervos

2016

Appl Math Optim

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We consider an irreversible capacity expansion model in which additional investment has a strictly negative effect on the value of an underlying stochastic economic indicator. The associated optimisation problem takes the form of a singular stochastic control problem that admits an explicit solution. A special characteristic of this stochastic control problem is that changes of the state process due to control action depend on the state process itself in a proportional way.

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“…Finally, we mention that previous work regarding problems with measures in one form or another appears in [2,6,7,10,15,[19][20][21][22][23][24][25][26]. Necessary conditions are derived in [22] and [25].…”

Section: Introductionmentioning

confidence: 99%