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

Huy\^en Pham
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Huy\^en Pham: LPMA, CREST

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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.

Date: 2016-04, Revised 2017-03
New Economics Papers: this item is included in nep-pke
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1604.06609

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