Existence of optimal controls for partially observed jump processes
type: Item
instance of: scholarly article
title: Existence of optimal controls for partially observed jump processes
zbMATH Open document ID: 1015.60075
DOI: 10.1023/A:1020669212384
author: Claudia Ceci
author: Anna Gerardi
author: Paola Tardelli
published in: Acta Applicandae Mathematicae
publication date: 2003-03-11T00:00:00Z
review text: This paper deals with a partially observable stochastic control problem for an \({\mathbb R}^d\)-valued Markov jump process \((X_t)\) given an observation process \((Y_t)\) which is a point process. In a previous paper [\textit{C. Ceci} and \textit{A. Gerardi}, Stochastic Processes Appl. 78, No.~2, 245-260 (1998; Zbl 0934.60077)], the authors have considered the case where \((Y_t)\) is the process that counts the jumps of \((X_s)\) up to time \(t\). In the present work they address the more general problem where \((X_t,Y_t)\) is a pure jump Markov process whose components may be strongly dependent. In particular no independence assumption is made on the intensities of \((X_t)\) and \((Y_t)\), which may have common jumps. They formulate the usual associated separated control problem in which the first component is a measure-valued process satisfying a controlled filtering equation. A relaxed generalized and totally observable control problem, for which an optimal strategy is determined, is stated by weakening the measurability assumptions on the control processes. Equivalence between the partially observable stochastic control problem and the relaxed generalized separated control problem is discussed. In particular it is proved that the infimum expected cost of the separated problem equals the infimum expected cost of the original problem, using a uniqueness result for the solutions of controlled filtering equations.
reviewed by: Nicolas Privault
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 1879600
zbMATH Keywords: jump processes
zbMATH Keywords: optimal stochastic control
zbMATH Keywords: partial observations
zbMATH Keywords: filtering
zbMATH Keywords: history sets
zbMATH Keywords: martingale problems
MaRDI profile type: Publication
full work available at URL: a:1020669212384
OpenAlex ID: W6686365
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description: scientific article; zbMATH DE number 1879600