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...

Hoogendoorn and Bovy (Transportation Research Part B, 2004, 38(7), 571– 592) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton-Jacobi-Bellman (HJB) equation that cont...

We prove the convergence of a non-monotonous scheme for a one-dimensional first order Hamilton-Jacobi-Bellman equation of the form vt+maxα(f(x, α)vx) = 0, v(0, x) = v0(x). The scheme is related to the HJB-UltraBee scheme suggested in [7]. We show for general discontinuous initial data a first-order convergence of the scheme, in L-norm, towards the viscosity solution. We also illustrate the non-...

This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose optimal to maximize expected return under uncertainty. The optimality condition, Hamilton–Jacobi–Bellman (HJB) equation, satisfied by value function and obtained dynamic programming method, is a partial differential equation coupled with One major computational difficulties irr...

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximat...

Many nonlinear option pricing problems can be formulated as optimal control problems, leading to Hamilton-Jacobi-Bellman (HJB) or Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. We show that such formulations are very convenient for developing monotone discretization methods which ensure convergence to the financially relevant solution, which in this case is the viscosity solution. In addition...

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 ...

The numerical realization of closed loop control for distributed parameter systems is still a significant challenge and in fact infeasible unless specific structural techniques are employed. In this paper we propose the combination of model reduction techniques based on proper orthogonal decomposition (POD) with the numerical treatment of the Hamilton–Jacobi–Bellman (HJB) equation for infinite ...

Many of the physical phenomena, like friction, backlash, drag, and etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control systems behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in friction various models. Simple inver...

The optimization of boiler soot blowing strategy and repair plan is investigated based on Hamilton–Jacobi–Bellman (HJB) equation in this paper. From the perspective soot, we build a Markov process with three modes to describe running process. For sake applying HJB equation, cost function constructed according built model, derived by using optimality principle. optimal can be obtained solving eq...