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We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…
In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first…
We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework.…
The aim of this paper is to study an optimal stopping problem for dynamic risk measures induced by backward stochastic differential equations with jumps and delayed generator. Firstly, we connect the value function of this problem to…
Switchback experiments, where a firm sequentially exposes an experimental unit to random treatments, are among the most prevalent designs used in the technology sector, with applications ranging from ride-hailing platforms to online…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…
This article deals with the starting and stopping problem under Knightian uncertainty, i.e., roughly speaking, when the probability under which the future evolves is not exactly known. We show that the lower price of a plant submitted to…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89-121] and generalized by Hamad\`ene and Zhang [Stochastic…
This paper extends our previous work to continuous-time optimal stopping, focusing on American options in an exploratory setting. Our first contribution is an entropy-regularized penalization scheme, inspired by classical penalization…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…
This paper is concerned with a general non-homogeneous stochastic linear quadratic (LQ) control problem with regime switching and random coefficients. We obtain the explicit optimal state feedback control and optimal value for this problem…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…