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Long-run risk sensitive dyadic impulse control

Author

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  • Marcin Pitera
  • {L}ukasz Stettner

Abstract

In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to combine geometric drift with local minorisation property in order to extend local span-contraction approach when the process as well as the linked reward/cost functions are unbounded. For any predefined risk-aversion parameter, the existence of solution to suitable Bellman equation is shown and linked to the underlying stochastic control problem. For completeness, examples of uncontrolled processes that satisfy the geometric drift assumption are provided.

Suggested Citation

  • Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive dyadic impulse control," Papers 1906.06389, arXiv.org.
    • Handle: RePEc:arx:papers:1906.06389
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    File URL: http://arxiv.org/pdf/1906.06389
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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 & 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. Damian Jelito & Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive impulse control," Papers 1912.02488, arXiv.org, revised Apr 2020.
    2. 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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