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Long-run risk sensitive impulse control

Author

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  • Damian Jelito
  • Marcin Pitera
  • {L}ukasz Stettner

Abstract

In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the underlying problem is constructed as a limit of dyadic impulse strategies by exploiting regularity properties of the linked risk sensitive optimal stopping value functions. In particular, this shows that the discretized setting could be used to approximate near optimal strategies for the underlying continuous time control problem, which facilitates the usage of the standard approximation tools. For completeness, we present examples of processes that could be embedded into our framework.

Suggested Citation

  • Damian Jelito & Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive impulse control," Papers 1912.02488, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1912.02488
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    References listed on IDEAS

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    1. Hideo Nagai, 2007. "A Remark on Impulse Control Problems with Risk-sensitive Criteria," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 13, pages 219-232, World Scientific Publishing Co. Pte. Ltd..
    2. Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive dyadic impulse control," Papers 1906.06389, arXiv.org.
    3. Ibtissam Hdhiri & Monia Karouf, 2011. "Risk sensitive impulse control of non-Markovian processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 1-20, August.
    4. Marcin Pitera & Łukasz Stettner, 2016. "Long run risk sensitive portfolio with general factors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 265-293, April.
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    Cited by:

    1. Jelito, Damian & Pitera, Marcin & Stettner, Łukasz, 2021. "Risk sensitive optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 125-144.

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