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Linear-quadratic McKean-Vlasov stochastic control problems with random coefficients on finite and infinite horizon, and applications
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We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic. Our method is based on a suitable extension of the martingale formulation for verification theorems in control theory. The optimal control involves the solution to a system of Riccati ordinary differential equations and to a linear mean-field backward stochastic differential equation, existence and uniqueness conditions are provided for such a system. Finally, we illustrate our results through two applications with explicit solutions: the first one deals with a portfolio liquidation problem with trade crowding, and the second one considers an economic model of substitutable production goods.
Forward citations
Cited by 2 Pith papers
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Convergence Rates of Time Discretization in Extended Mean Field Control
For linear-convex extended mean field control, piecewise constant controls approximate the optimal cost at rate 1/2 and the optimal control at rate 1/4; under smoothness, the rate improves to 1.
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A new probabilistic approach for mean field games of optimal stopping
Randomized mean-field equilibria of optimal-stopping games are characterized by a coupled reflected McKean–Vlasov forward-backward SDE system whose survival process L is an endogenous part of the solution.
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