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In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…
This paper studies dynamic mean-variance (MV) asset allocation problems in general incomplete markets. Besides of the conventional MV objective on portfolio's terminal wealth, our framework can accommodate running MV objectives with general…
We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach…
Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
In this article, we analyse the existence of an optimal feedback controller of stochastic optimal control problems governed by SDEs which have the control in the diffusion part. To this end, we consider the underlying Fokker-Planck equation…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
We investigate time-inconsistent portfolio problems under a broader class of monotone mean-variance (MMV) preferences. Since the optimal strategies for MMV and mean-variance (MV) preferences coincide, the MMV optimal strategies at different…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…