Optimal Models with Maximizing the Probability of First Achieving Target Value in the Preceding Stages

Lin, Y; Wu, C; Kang, B

Optimal Models with Maximizing the Probability of First Achieving Target Value in the Preceding Stages

Lin, Y Wu, C Kang, B

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Publisher:: Zhongguo Kexue Zazhishe
Publication Type:: Journal Article
Citation:: Science In China Series A, 2003, 46 (3), pp. 396 - 414
Issue Date:: 2003-01

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Field	Value	Language
dc.contributor.author	Lin, Y	en_US
dc.contributor.author	Wu, C	en_US
dc.contributor.author	Kang, B	en_US
dc.date.issued	2003-01	en_US
dc.identifier.citation	Science In China Series A, 2003, 46 (3), pp. 396 - 414	en_US
dc.identifier.issn	1006-9283	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8285
dc.description.abstract	Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of ?-optimal policy for finite state space. We give an example for the reliability of the satellite systems using the above theory. Finally, we extend these results to more general cases.	en_US
dc.publisher	Zhongguo Kexue Zazhishe	en_US
dc.relation.ispartof	Science In China Series A	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Optimal Models with Maximizing the Probability of First Achieving Target Value in the Preceding Stages	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	46	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
utslib.copyright.status	closed_access
pubs.consider-herdc	false	en_US
pubs.issue	3	en_US
pubs.volume	46	en_US

Abstract:

Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of ?-optimal policy for finite state space. We give an example for the reliability of the satellite systems using the above theory. Finally, we extend these results to more general cases.

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http://hdl.handle.net/10453/8285