相关论文: Viscosity solutions for obstacle problems on Wasse…
This paper is devoted to solving a class of second order Hamilton-Jacobi-Bellman (HJB) equations in the Wasserstein space, associated with mean field control problems involving common noise. The well-posedness of viscosity solutions to the…
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves leveraging differentiability properties of the…
This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming…
We establish the well-posedness of viscosity solutions for a class of semi-linear Hamilton-Jacobi equations set on the space of probability measures on the torus. In particular, we focus on equations with both common and idiosyncratic…
This work concerns the optimal control problem for McKean-Vlasov SDEs. In order to characterize the value function, we develop the viscosity solution theory for Hamilton-Jacobi-Bellman (HJB) equations on the Wasserstein space using…
Dynamic programming equations for mean field control problems with a separable structure are Eikonal equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity…
The aim of this article is twofold. First, we develop a unified framework for viscosity solutions to both first-order Hamilton-Jacobi equations and semilinear Hamilton-Jacobi equations driven by the idiosyncratic operator, defined on the…
In this paper, we prove a comparison result for semi-continuous viscosity solutions of a class of second-order PDEs in the Wasserstein space. This allows us to remove the Lipschitz continuity assumption with respect to the…
This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron's method, i.e. via showing that the supremum of viscosity subsolutions is a viscosity solution. We use the notion of viscosity solutions…
We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient…
We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define…
We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. Specifically, we obtain the viscosity property of value functions, the uniqueness of viscosity solutions, the regularity of value…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in $(t,\omega)$, and generator Lipschitz continuous in $(y,z,\gamma)$. We prove…
The main result of this paper is to prove that viscosity solutions to a parabolic free boundary problem with variable coefficients are Lipschitz continuous under the assumptions that the solution has a Lipschitz free boundary and satisfies…
We study viscosity solutions to a system of nonlinear degenerate parabolic partial integro-differential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of…
This paper explores the application of nonsmooth analysis in the Wasserstein space to finite-horizon optimal control problems for nonlocal continuity equations. We characterize the value function as a strict viscosity solution of the…
In this paper we analyze the optimal value function $v$ associated to a general parametric optimization problems via the theory of viscosity solutions. The novelty is that we obtain regularity properties of $v$ by showing that it is a…
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we prove the two important results till now…