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Singular stochastic control and optimal stopping with partial information of Itô--Lévy processes

Author

Listed:
  • Bernt Oksendal

    (CMA - Center of Mathematics for Applications [Oslo] - Department of Mathematics [Oslo] - Faculty of Mathematics and Natural Sciences [Oslo] - UiO - University of Oslo)

  • Agnès Sulem

    (MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12)

Abstract

We study partial information, possibly non-Markovian, singular stochastic control of Itô--Lévy processes and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. As an application we give an explicit solution to a class of optimal stopping problems with finite horizon and partial information.

Suggested Citation

  • Bernt Oksendal & Agnès Sulem, 2011. "Singular stochastic control and optimal stopping with partial information of Itô--Lévy processes," Working Papers inria-00614279, HAL.
    • Handle: RePEc:hal:wpaper:inria-00614279
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00614279
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    References listed on IDEAS

    as
    1. Boetius, Frederik & Kohlmann, Michael, 1998. "Connections between optimal stopping and singular stochastic control," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 253-281, September.
    2. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Singular stochastic control; maximum principles; reflected BSDEs; optimal stopping; partial information; Itô--Lévy processes; jump diffusions;
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