Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time projected state-space grid. The use structured grid makes this approach not feasible high-dimensional problems due to curse dimensionality. Here, we present new infinite horizon optimal control where value function is computed using Radial Basis Functions (RBF) by Shepard's moving least squares a...

This thesis looks at a few different approaches to solving stochastic optimal control problems with state constraints. The motivating problem is optimal control of an energy buffer in a hybrid vehicle, although applications are abundant in a number of areas. Stochastic optimal control problems can be solved via the socalled Hamilton-Jacobi-Bellman (HJB) equation. State constraints result in bou...

We consider the optimal dividend problem in so-called degenerate bivariate risk model under assumption that surplus of one branch may become negative. More specific, we solve stochastic control maximizing discounted dividends until simultaneous ruin both branches an insurance company by showing value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, prove is smallest...

INTRODUCTION The jugular bulb is found at the junction of the horizontal segment of the sigmoid sinus and the superior end of the internal jugular vein. A high jugular bulb (HJB) may extend into the middle ear cavity lateral to the cochlea. The superior threshold of HJB varies according to various authors. The limits include the inferior bony annulus, the lower border of the round window, and t...

In this paper we develop a new method to approximate the solution to the Hamilton-JacobiBellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial di erential equations. These equations are then approximated ...

The purpose of this paper is to describe the application of the notion of viscosity solutions to solve the Hamilton–Jacobi–Bellman (HJB) equation associated with an important class of optimal control problems for quantum spin systems. The HJB equation that arises in the control problems of interest is a first-order nonlinear partial differential equation defined on a Lie group. Hence we employ ...

In this paper, we consider the optimal investment problem for an insurer who has n dependent lines of business. The surplus process of the insurer is described by a n-dimensional compound Poisson risk process. Moreover, the insurer is allowed to invest in a risk-free asset and a risky asset whose price process follows the constant elasticity of variance (CEV) model. The investment objective is ...