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

Huyên Pham
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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 - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Stochastic McKean-Vlasov SDEs; random coefficients; linear quadratic op-timal control; dynamic programming; Riccati equation; backward stochastic differential equation (search for similar items in EconPapers)
Date: 2016-12
Note: View the original document on HAL open archive server: https://hal.science/hal-01305929v2
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Published in Probability, Uncertainty and Quantitative Risk, 2016, 1 (1), pp.7. ⟨10.1186/s41546-016-0008-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01305929

DOI: 10.1186/s41546-016-0008-x

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