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Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting

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  • T Kruse

    (Universität Duisburg-Essen = University of Duisburg-Essen [Essen])

  • A Popier

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

Abstract

We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +∞ with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity assumption. With this minimal supersolution we then solve an optimal stochastic control problem related to portfolio liquidation problems. We generalize the existing results in three directions: firstly there is no assumption on the underlying filtration (except completeness and quasi-left continuity), secondly we relax the terminal liquidation constraint and finally the time horizon can be random.

Suggested Citation

  • T Kruse & A Popier, 2015. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Working Papers hal-01139364, HAL.
    • Handle: RePEc:hal:wpaper:hal-01139364
    Note: View the original document on HAL open archive server: https://hal.science/hal-01139364v2
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    References listed on IDEAS

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    1. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
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