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

Huyên Pham

doi:10.1186/s41546-016-0008-x

Article Contents

2016, Volume 1: 7. Doi: 10.1186/s41546-016-0008-x

This volume Previous Article Backward-forward linear-quadratic mean-field games with major and minor agents Next Article Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs

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

Huyên Pham^1,2

1 Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot, Paris, France;
2 CREST-ENSAE, Paris, France

Received: April 25, 2016

Revised: August 10, 2016

Published: September 2020

Abstract / Introduction Related Papers Cited by

Abstract

We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional. The coefficients of the system and the weighting 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 (Pham and Wei, Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics, 2016), 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 an incomplete market model.

Keywords:

Stochastic McKean-Vlasov SDEs,
Random coefficients,
Linear quadratic optimal control,
Dynamic programming,
Riccati equation,
Backward stochastic differential equation.

Mathematics Subject Classification: 49N10;49L20;60H10;93E20.

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