In this chapter we discuss combined optimal stop** and stochastic control problems and
their associated Hamilton–Jacobi–Bellman (HJB) variational inequalities. This is a subject …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

We study a stochastic optimal control problem for a delayed Markov regime-switching jump-
diffusion model. We establish necessary and sufficient maximum principles under full and …

This paper investigates a stochastic optimal control problem with delay and of mean-field
type, where the controlled state process is governed by a mean-field jump–diffusion …

This paper examines the long-standing problem of linear quadratic regulation and
stabilization for Itô stochastic systems with input delay. This problem remains a primary …

We propose a model of inter-bank lending and borrowing which takes into account clearing
debt obligations. The evolution of log-monetary reserves of banks is described by coupled …

This study examines the scientific production focused on the Maximum Principle between
1962 and 2021. Results indicate a consistent increase in the absolute number of …

We extend the taming techniques for explicit Euler approximations of stochastic differential
equations driven by Lévy noise with superlinearly growing drift coefficients. Strong …

Stochastic control problems with delay are challenging due to the path-dependent feature of
the system and thus its intrinsic high dimensions. In this paper, we propose and …

In this article, we consider a linear-quadratic mean field game between a leader (dominating
player) and a group of followers (agents) under the Stackelberg game setting as proposed in …