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The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
This paper studies the continuous-time reinforcement learning for stochastic singular control with the application to an infinite-horizon irreversible reinsurance problems. The singular control is equivalently characterized as a pair of…
This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and…
In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients,…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum…
The general maximum principle is proved for an infinite dimensional controlled stochastic evolution system. The control is allowed to take values in a nonconvex set and enter into both drift and diffusion terms. The operator-valued backward…
Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a…
This paper focuses on the discrete-time backward stochastic linear quadratic (BSLQ) optimal control problem with nonhomogeneous system terms and cost function cross terms. The terminal constraint of such systems distinguishes it from…
This paper studies an optimal consumption problem with both relaxed benchmark tracking and consumption drawdown constraint, leading to a stochastic control problem with dynamic state-control constraints. In our relaxed tracking formulation,…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
For a class of stochastic delay evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. The delays are given as moving averages with…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
This paper investigates the solvability and optimal control of a class of impulsive stochastic differential equations (SDEs) within a Hilbert space setting. First, we establish the existence and uniqueness of mild solutions for the proposed…
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…