On impulse control with partial observation

Mazziotto, G.; Stettner, Łukasz; Szpirglas, J.; Zabczyk, Jerzy

doi:10.1007/bfb0005085

Cited by 6 publications

(11 citation statements)

References 3 publications

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“…We prove that the costs associated with the sequence of impulse control problems converge Downloaded by [National Sun Yat-Sen University] at 18: 46 27 December 2014 towards that of the continuous control problem. Each of these impulse control problems with partial observation can be explicitly solved by using the results of [38] or [39]. Thus, we obtain identical infima of the expected cost over the set V of admissible controls and the set & of separated controls (similar result in weak formulation can be found in [20]).…”

Section: Introductionmentioning

confidence: 81%

“…be the family of filtering processes associated with {R',";E E}. It can be proved as in [38] or [39] that the following relation, involving the filtering process fi, holds on {T, 5 t < T, + , ):…”

Section: Set Fib=tj Xiexrb ~ = B ( U ) @ B ( I E ) @ B T and V Amentioning

confidence: 97%

“…By using the results obtained in [38] and [39] for the impulse control of partially observed systems, we explicitly construct a sequence of controls in separated form. We then prove that the optimal cost for the partially observed continuous problem can be approximated as closely as desired by those of impulse control problems.…”

Section: Approximation O F a Stochastic Continuous Problem By Impulsementioning

confidence: 99%

“…This framework has been developed in various contributions, but we will mainly be referring to the approach of [39]. The admissible controls are all the Y-progressively measurable processes u=(u,; t €10, a [ ) defined on (Ry,Y,, PY) with values in a given compact metric set U endowed with its Borel a-field g(U).…”

Section: General Definitions and Propertiesmentioning

confidence: 99%

“…[38] or [39] for the case of partially observed systems). For each E, the optimal control depends causally on the filtering process of the system.…”

mentioning

confidence: 98%

See 4 more Smart Citations

Stochastic continuous control of partially observed systems via impulse control problems

Cohen¹,

Mazziotto²

1989

Stochastics and Stochastic Reports

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The stochastic control problem of partially observed systems is approximated by a sequence of partially observed impulse control problems with non-zero but vanishing impulse costs. For the latter problems, we give an explicit construction of the so-called &-optimal controls in a separated form.As a consequence of this approach, we prove that the infimum of the expected cost over the set of separated controls-i.e. which depend non anticipatively on the filtering process-is equal to the infimum of the expected cost over the set of admissible controls-i.e. which depend non anticipatively on the observation process.For the classical situation of linear systems, this method yields the existence of an optimal separated control.

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Section: Introductionmentioning

confidence: 81%

Section: Set Fib=tj Xiexrb ~ = B ( U ) @ B ( I E ) @ B T and V Amentioning

confidence: 97%

Section: Approximation O F a Stochastic Continuous Problem By Impulsementioning

confidence: 99%

Section: General Definitions and Propertiesmentioning

confidence: 99%

“…[38] or [39] for the case of partially observed systems). For each E, the optimal control depends causally on the filtering process of the system.…”

mentioning

confidence: 98%

See 3 more Smart Citations

Stochastic continuous control of partially observed systems via impulse control problems

Cohen¹,

Mazziotto²

1989

Stochastics and Stochastic Reports

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Sequential tracking of a hidden Markov chain using point process observations

Bayraktar

Ludkovski

2009

Stochastic Processes and their Applications

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We study finite horizon optimal switching problems for hidden Markov chain models with point process observations. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state variable using Bayesian updates over the discrete observations. Such a model has applications in economic policy making, staffing under variable demand levels and generalized Poisson disorder problems. We show regularity of the value function and explicitly characterize an optimal strategy. We also provide an efficient numerical scheme and illustrate our results with several computational examples.

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A simulation approach to optimal stopping under partial information

Ludkovski

2009

Stochastic Processes and their Applications

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We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional diffusion with correlated noise. Such models where the controller is not fully aware of her environment are of interest in applied probability and financial mathematics. We propose a new approximate numerical algorithm based on the particle filtering and regression Monte Carlo methods. The algorithm maintains a continuous state-space and yields an integrated approach to the filtering and control sub-problems. Our approach is entirely simulation-based and therefore allows for a robust implementation with respect to model specification. We carry out the error analysis of our scheme and illustrate with several computational examples. An extension to discretely observed stochastic volatility models is also considered.Date: October 31, 2018.

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On impulse control with partial observation

Cited by 6 publications

References 3 publications

Stochastic continuous control of partially observed systems via impulse control problems

Stochastic continuous control of partially observed systems via impulse control problems

Sequential tracking of a hidden Markov chain using point process observations

A simulation approach to optimal stopping under partial information

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