There are two main parts of this thesis: Time-Inconsistent Control (TIC) problems (Chapters 1 and 2) and the neural network approximation (Chapters 3 and 4). In the first part of the thesis, we are interested in constructing and characterizing the equilibria of TIC problems, while in the second part of the thesis, we apply the neural network approach to solve path-dependent Partial Differential Equations (PDEs) and derive the generalization error bounds of 2-layer neural networks. More precisely, in Chapter 1 we extend the construction of equilibria for mean-variance portfolio and linear-quadratic problems available in the literature to a large class of mean-field continuous-time TIC problems. Our approach relies on a time discretization...
We consider a deterministic optimal control problem with a maximum running cost functional, in a fin...
We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks ...
This paper presents a dynamical neural network approach to solve stochastic two-players zero-sum gam...
Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi...
The present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial di...
In this paper, we establish that for a wide class of controlled stochastic differential equations (S...
An optimal control problem is considered for a stochastic differential equation with the cost functi...
The present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial di...
In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman...
We study the optimal control in a long time horizon of neural ordinary differential equations which ...
Artificial neural networks are generally employed in the numerical solution of differential equation...
We discuss the numerical solution to a class of continuous time finite state mean field games. We ap...
An optimal control problem is considered for a stochastic differential equation containing a state-d...
26 pages, to appear in SIAM Journal of Scientific ComputingRecently proposed numerical algorithms f...
In this article, we consider the linear-quadratic time-inconsistent mean-field type leader-follower ...
We consider a deterministic optimal control problem with a maximum running cost functional, in a fin...
We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks ...
This paper presents a dynamical neural network approach to solve stochastic two-players zero-sum gam...
Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi...
The present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial di...
In this paper, we establish that for a wide class of controlled stochastic differential equations (S...
An optimal control problem is considered for a stochastic differential equation with the cost functi...
The present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial di...
In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman...
We study the optimal control in a long time horizon of neural ordinary differential equations which ...
Artificial neural networks are generally employed in the numerical solution of differential equation...
We discuss the numerical solution to a class of continuous time finite state mean field games. We ap...
An optimal control problem is considered for a stochastic differential equation containing a state-d...
26 pages, to appear in SIAM Journal of Scientific ComputingRecently proposed numerical algorithms f...
In this article, we consider the linear-quadratic time-inconsistent mean-field type leader-follower ...
We consider a deterministic optimal control problem with a maximum running cost functional, in a fin...
We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks ...
This paper presents a dynamical neural network approach to solve stochastic two-players zero-sum gam...