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Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications

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  • Huyên Pham

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.

Suggested Citation

  • Huyên Pham, 2016. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Post-Print hal-01305929, HAL.
    • Handle: RePEc:hal:journl:hal-01305929
    DOI: 10.1186/s41546-016-0008-x
    Note: View the original document on HAL open archive server: https://hal.science/hal-01305929v2
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    References listed on IDEAS

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    1. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    2. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
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    Cited by:

    1. Gianmarco Del Sarto & Marta Leocata & Giulia Livieri, 2024. "A Mean Field Game approach for pollution regulation of competitive firms," Papers 2407.12754, arXiv.org.

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