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Successive Approximations for Finite Horizon, Semi-Markov Decision Processes with Application to Asset Liquidation

Author

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  • John W. Mamer

    (University of California, Los Angeles, Los Angeles, California)

Abstract

This paper presents a simple successive approximation approach to the characterization of optimal policies for finite horizon, semi-Markov decision processes. Optimal policies are nonstationary, for in this setting they depend on both time and state. We illustrate this approach by analyzing the optimal liquidation of an asset; we also show that several aspects of the standard, discrete-time, infinite horizon optimal policy carry over to the continuous-time, finite horizon policy.

Suggested Citation

  • John W. Mamer, 1986. "Successive Approximations for Finite Horizon, Semi-Markov Decision Processes with Application to Asset Liquidation," Operations Research, INFORMS, vol. 34(4), pages 638-644, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:638-644
    DOI: 10.1287/opre.34.4.638
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    Cited by:

    1. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.
    2. Huang, Yonghui & Guo, Xianping, 2011. "Finite horizon semi-Markov decision processes with application to maintenance systems," European Journal of Operational Research, Elsevier, vol. 212(1), pages 131-140, July.
    3. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    4. Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.
    5. Zhang, Xueqing & Gao, Hui, 2012. "Road maintenance optimization through a discrete-time semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 110-119.
    6. Turner, Rolf & Banerjee, Pradeep & Shahlori, Rayomand, 2014. "Optimal Asset Pricing," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i11).
    7. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    8. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    9. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    10. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    11. Zhao, Yunfei & Huang, Linan & Smidts, Carol & Zhu, Quanyan, 2020. "Finite-horizon semi-Markov game for time-sensitive attack response and probabilistic risk assessment in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    12. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    13. Banerjee, Pradeep K. & Turner, T. Rolf, 2012. "A flexible model for the pricing of perishable assets," Omega, Elsevier, vol. 40(5), pages 533-540.

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