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

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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.
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Dates and versions

hal-01305929 , version 1 (22-04-2016)
hal-01305929 , version 2 (07-03-2017)

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Huyên Pham. Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *. 2017. ⟨hal-01305929v2⟩
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