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Switching problems with controlled randomisation and associated obliquely reflected BSDEs

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  • Bénézet, Cyril
  • Chassagneux, Jean-François
  • Richou, Adrien

Abstract

We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value of the switching problem is related to a new class of multidimensional obliquely reflected BSDEs. These BSDEs allow as well to construct an optimal strategy and thus to solve completely the initial problem. The other main contribution of our work is to prove new existence and uniqueness results for these obliquely reflected BSDEs. This is achieved by a careful study of the domain of reflection and the construction of an appropriate oblique reflection operator in order to invoke results from Jean-François Chassagneux and Adrien Richou (2020).

Suggested Citation

  • Bénézet, Cyril & Chassagneux, Jean-François & Richou, Adrien, 2022. "Switching problems with controlled randomisation and associated obliquely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 23-71.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:23-71
    DOI: 10.1016/j.spa.2021.10.010
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    1. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    4. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    5. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    6. Randall Martyr, 2016. "Finite-Horizon Optimal Multiple Switching with Signed Switching Costs," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1432-1447, November.
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    Cited by:

    1. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.

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