Related papers: Verification Theorems for Hamilton-Jacobi-Bellman …
We study an optimal stopping problem when the state process is governed by a general Feller process. In particular, we examine viscosity properties of the associated value function with no a priori assumption on the stochastic differential…
In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the…
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…
In the paper we study the following problem: given a Hamilton-Jacobi equation where the Hamiltonian is convex with respect to the last variable, are there any optimal control problems representing it? In other words, we search for an…
We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
In standard treatments of stochastic filtering one first has to estimate the values of the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional…
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here,…
This paper develops a framework for establishing the existence of solutions to the equilibrium Hamilton-Jacobi-Bellman (EHJB) equation arising in time-inconsistent stochastic control problems. The time-inconsistency in our setting arises…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…