Discrete-time multiparameter fractional optimal stopping problems
*Teruo TanakaCorresponding authorteruo@hiroshima-cu.ac.jpDepartment of Systems EngineeringGraduate School of Information Sciences3-4-1, OzukahigashiHiroshima City UniversityAsaminami-ku, Hiroshima, 731-3194, JapanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jun 2022
- Accepted:
- 08 Nov 2022
- Published Online:
- 23 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1327
- Pages:
- 1213–1221
Abstract
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References
[1] Vijay Kumar Aggarwal, Ramaswamy Chandrasekaran, and Kunhiraman P. K. Nair, “Markov ratio decision processes,” Journal of Optimization Theory and Applications, vol. 21, pp. 27–37 (1977).
[2] Renzo Cairoli and Robert C. Dalang, Sequential Stochastic Optimization. New York, NY, USA: John Wiley & Sons, Inc. (1996).
[3] Seiichi Iwamoto and Toshiharu Fujita, “Markov decision processes under fractional criteria,” Kyoto University RIMS Kokyuroku, no. 1079, pp. 153–163 (1999) (in Japanese).
[4] Ulrich Krengel and Louis Sucheston, “Stopping rules and tactics for processes indexed by a directed set,” Journal of Multivariate Analysis, vol. 11, pp. 199–229 (1981).
[5] Gregory F. Lawler and Robert Joseph Vanderbei, “Markov strategies for optimal control over partially ordered sets,” The Annals of Probability, vol. 11, pp. 642–647 (1983).
[6] Avi Mandelbaum, “Discrete multi-armed bandits and multi-parameter processes,” Probability Theory and Related Fields, vol. 71, pp. 129–147 (1986).
[7] Avi Mandelbaum and Robert Joseph Vanderbei, “Optimal stopping and supermartingales over partially ordered sets,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 57, pp. 253–264 (1981).
[8] Gérald Mazziotto, “Two-parameter optimal stopping and bi-Markov processes,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 69, pp. 99–135 (1985).
[9] Hiroaki Morimoto, “On average cost stopping time problems,” Probability Theory and Related Fields, vol. 90, pp. 469–490 (1991).
[10] Zhiyuan Ren and Bruce Krogh, “Markov decision processes with fractional costs,” IEEE Transactions on Automatic Control, vol. 50, pp. 646–650 (2005).
[11] Yoichi Sawasaki, Yutaka Kimura, and Kensuke Tanaka, “A two-person zero-sum game with fractional loss function,” Journal of the Operations Research Society of Japan, vol. 43, pp. 209–218 (2000).
[12] Ioan Mihai Stancu-Minasian, Fractional Programming. Dordrecht, The Netherlands: Kluwer Academic Publishers (1997).
[13] Teruo Tanaka, “Fakeev’s necessary conditions for optimality in multi-parameter optimal stopping problems,” Journal of Information and Optimization Sciences, vol. 39, no. 8, pp. 1627–1636 (2018).
[14] Teruo Tanaka, “A D-solution of a multi-parameter continuous-time optimal stopping problem with constraints,” Journal of Information and Optimization Sciences, vol. 40, no. 4, pp. 839–852 (2019).
