We investigate a continuous-time mean–variance portfolio selection problem. Different from the general stochastic dynamic programming approach, such as using Hamilton–Jacobi–Bellman (HJB) equation, this paper adopts the Lagrange duality method and the finite difference approach to derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient front...

We study a class of optimal control problems with state constraint, where the state equation is a differential equation with delays in the control variable. This class of problems arises in some economic applications, in particular in optimal advertising problems. The optimal control problem is embedded in a suitable Hilbert space, and the associated Hamilton–Jacobi–Bellman (HJB) equation is co...

Abstract Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in unconstrained case. Here we analyze case with constraints both for HJB equations arise deterministic and stochastic cases. The linear each step are solved by an implicit upw...

This paper presents a novel approach for developing tracking controllers for nonlinear systems. The approach involves the numerical solution, by Galerkin approximation , of the time-varying Hamilton-Jacobi-Bellman (HJB) equation and results in a nonlinear controller approximating the optimal tracking control law for a spec-iied desired trajectory and cost function. Experimental results are pres...

In this paper, an iterative algorithm to solve a special class of Hamilton-JacobiBellman-Isaacs (HJBI) equations is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local converge...

Abstract. The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton–Jacobi– Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White’s ‘relative value iteration’ ...

In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton–Jacobi–Bellman (HJB) equations and we compare the results with an accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be indeed used to solve HJB equations with no relevant modifications with respect to the original algorithm proposed for the eikonal equation, and that it overcomes FSM in...

Abstract: Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items. Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem. Results: It was then illustrated with the help ...

An optimal finite-time horizon feedback control problem for (semi-linear) wave equations is presented. The feedback law can be derived from the dynamic programming principle and requires to solve the evolutionary Hamilton-Jacobi-Bellman (HJB) equation. Classical discretization methods based on finite elements lead to approximated problems governed by ODEs in high dimensional spaces which makes ...

We study the stochastic Hamilton–Jacobi–Bellman (HJB) equation with jump, which arises from a non-Markovian optimal control problem recursive utility cost functional. The solution to is predictable triplet of random fields. show that value function problem, under some regularity assumptions, HJB equation; and classical this characterizes control. With additional assumptions on coefficients, an ...