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Discrete-time risk-aware optimal switching with non-adapted costs

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Listed:
  • Randall Martyr

    (Queen Mary University of London)

  • John Moriarty

    (Queen Mary University of London)

  • Magnus Perninge

    (Linnaeus University)

Abstract

We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example application to hydropower planning is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1910.04047
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    3. 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.
    4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    5. Nicole Bäauerle & Ulrich Rieder, 2017. "Partially Observable Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1180-1196, November.
    6. 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.
    7. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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