相关论文: Expected Utility Optimization - Calculus of Variat…
In this paper, we study the following nonlinear backward stochastic integral partial differential equation with jumps \begin{equation*} \left\{ \begin{split} -d V(t,x) =&\displaystyle\inf_{u\in U}\bigg\{H(t,x,u, DV(t,x),D \Phi(t,x), D^2…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…
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…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
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 show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using…
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions…
In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
In this article, we study optimal feedback control synthesis of stochastic 2D Navier-Stokes equations perturbed Levy type noise with distributed stochastic control process acting on the state equation. We use the dynamic programming…
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the…
This paper is a review of results on Optimisation which are perhaps not so standard in the PDE realm. To this end, we consider the problem of deriving the PDEs associated to the optimal control of a system of either ODEs or SDEs with…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
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…