相关论文: Viscosity Solutions in Non-commutative Variables

The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…

We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…

We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise model is additive. In this work, we address certain non-additive…

We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…

This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…

This paper develops a comparison theorem for viscosity solutions of a new class of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the separated problem governed by the K-S equation in the Wasserstein space. A distinctive…

In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…

This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process…

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be H\"older continuous, with a modulus depending only on the growth of the…

Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert spaces. The notion of viscosity solution without…

Optimal control of heterogeneous mean-field stochastic differential equations with common noise has not been addressed in the literature. In this work, we initiate the study of such models. We formulate the problem within a linear-quadratic…

We establish the existence and uniqueness of viscosity solutions within a domain $\Omega\subseteq\mathbb R^n$ for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from…

We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo's classical viability theorems (necessary and sufficient conditions for mean viability). As an application, we…

A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…

In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing…

In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This HJB equation is related to a stochastic optimal control problem for which…

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…

We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…