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Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Open Access Research Article

Continuous time optimal stopping problems with fractional rewards

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pp. 2057–2062Vol. 46Issue 7October 2025DOI: 10.47974/JIOS-1328XML
Received:
08 Jun 2022
Accepted:
02 Nov 2022
Published Online:
18 Jul 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1328
Pages:
2057–2062

Abstract

We consider fractional, or average reward, optimal stopping problems for continuous time stochastic processes. We extend the results in Morimoto [4] to the general case, and then state the characterization of optimal value and optimal stopping time and the efficiency of Denkelbach algorithm for searching an optimal stopping time.

Keywords

Subject Classifications

60G4093E20

References

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[4] Hiroaki Morimoto, “On average cost stopping time problems,” Probability Theory and Related Fields, vol. 90, pp. 469–490 (1991).
[5] Zhiyuan Ren and Bruce Krogh, “Markov decision processes with fractional costs,” IEEE Transactions on Automatic Control, vol. 50, pp. 646–650 (2005).
[6] 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).
[7] Ioan Mihai Stancu–Minasian, Fractional Programming. Dordrecht, The Netherlands: Kluwer Academic Publishers (1997).
[8] Teruo Tanaka, “Optimal stochastic sequential control with fractional rewards,” Journal of Statistics and Management Systems, vol. 21, no. 7, pp. 1173–1188 (2018).

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