Related papers: On Singular Control Problems with State Constraint…
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set…
This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex.…
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price…
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections…
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \[ \left\{\begin{array} [c]{r} dX(t)+\partial\varphi\left(X(t)\right)…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
We study a stochastic control problem with regime switching arising in an optimal liquidation problem with dark pools and multiple regimes. The new feature of this model is that it introduces a system of BSDEs with jumps and with singular…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…
We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…
We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…