The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniqu...

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...

We propose a method for calibrating a volatility surface that matches option prices using an entropy-inspired framework. Starting with a stochastic volatility model for asset prices, we cast the estimation problem as a variational one and we derive a Hamilton-Jacobi-Bellman (HJB) equation for the volatility surface. We study the asymptotics of the HJB equation assuming that the stochastic volat...

In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with s...

This paper is concerned with mean-variance portfolio selection problems in continuoustime under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the no-shorting restr...

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...

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...

In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general insurance models to queueing theory. The main novel point of such a control problem is that by changing the jump size of the system, one essentially changes the...

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth timedependent Hamilton-Jacobi-Bellman (HJB) equation is solved by regularization and the application of a semi-smooth Newton method. Discretization in space is carried out by finite differen...

In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from the dynamic programming approach. However, the bottleneck is mainly due to the curse of dime...