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Optimal Stochastic Control Problem Under Model Uncertainty With Nonentropy Penalty

Author

Listed:
  • WAHID FAIDI

    (Laboratoire de Modélisation Mathématique et Numérique, dans les Sciences de l’Ingénieur, ENIT, University of Tunis El Manar, Tunisia)

  • ANIS MATOUSSI

    (Laboratoire Manceau de Mathématiques, Institut du Risque et de l’Assurance, Université du Maine, US)

  • MOHAMED MNIF

    (Laboratoire de Modélisation Mathématique et Numérique, dans les Sciences de l’Ingénieur, ENIT, University of Tunis El Manar, Tunisia)

Abstract

In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty is studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.

Suggested Citation

  • Wahid Faidi & Anis Matoussi & Mohamed Mnif, 2017. "Optimal Stochastic Control Problem Under Model Uncertainty With Nonentropy Penalty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-41, May.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500157
    DOI: 10.1142/S0219024917500157
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    References listed on IDEAS

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    Cited by:

    1. Wahid Faidi, 2022. "Optimal investment and consumption under logarithmic utility and uncertainty model," Papers 2211.05367, arXiv.org.
    2. Dejian Tian, 2022. "Pricing principle via Tsallis relative entropy in incomplete market," Papers 2201.05316, arXiv.org, revised Oct 2022.

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