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Risk measurement and risk-averse control of partially observable discrete-time Markov systems

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  • Jingnan Fan

    (Rutgers University)

  • Andrzej Ruszczyński

    (Rutgers University)

Abstract

We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.

Suggested Citation

  • Jingnan Fan & Andrzej Ruszczyński, 2018. "Risk measurement and risk-averse control of partially observable discrete-time Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 161-184, October.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:2:d:10.1007_s00186-018-0633-5
    DOI: 10.1007/s00186-018-0633-5
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    References listed on IDEAS

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    1. Jingnan Fan & Andrzej Ruszczynski, 2014. "Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems," Papers 1411.2675, arXiv.org, revised Nov 2016.
    2. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    3. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    4. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    5. A. Jobert & L. C. G. Rogers, 2008. "Valuations And Dynamic Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 1-22, January.
    6. Runggaldier, Wolfgang J., 1998. "Concepts and methods for discrete and continuous time control under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 25-39, May.
    7. Mannor, Shie & Tsitsiklis, John N., 2013. "Algorithmic aspects of mean–variance optimization in Markov decision processes," European Journal of Operational Research, Elsevier, vol. 231(3), pages 645-653.
    8. Nicole Bäauerle & Ulrich Rieder, 2017. "Partially Observable Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1180-1196, November.
    9. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627, October.
    10. Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612, October.
    11. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    12. Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    13. Eugene A. Feinberg & Pavlo O. Kasyanov & Michael Z. Zgurovsky, 2016. "Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 656-681, May.
    14. Jerzy A. Filar & L. C. M. Kallenberg & Huey-Miin Lee, 1989. "Variance-Penalized Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 147-161, February.
    15. A. Jaśkiewicz & J. Matkowski & A. S. Nowak, 2013. "Persistently Optimal Policies in Stochastic Dynamic Programming with Generalized Discounting," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 108-121, February.
    16. Chen, Zhiping & Li, Gang & Zhao, Yonggan, 2014. "Time-consistent investment policies in Markovian markets: A case of mean–variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 293-316.
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    Cited by:

    1. Tomasz R. Bielecki & Igor Cialenco & Andrzej Ruszczy'nski, 2022. "Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty," Papers 2206.09235, arXiv.org.
    2. Randall Martyr & John Moriarty & Magnus Perninge, 2019. "Discrete-time risk-aware optimal switching with non-adapted costs," Papers 1910.04047, arXiv.org, revised Sep 2021.

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