We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky asset. Using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman (HJB) equation, obta...

Private sector operators of response services such as ambulance, fire or police etc. are often regulated by targets on the distribution of response times. This may result in inefficient overstaffing to ensure those targets are met. In this paper, we use a network chain of M/M/K queues to model the arrival and completion of jobs on the system so that quantities such as the expected total time wa...

This paper proposes a tracking control method for a differential drive wheeled mobile robot with nonholonomic constraints with an inverse optimal neural controller. It is based on two techniques: first, an identifier using a discrete-time recurrent high-order neural network (RHONN) trained with an extended Kalman filter (EKF) algorithm is employed; second, an inverse optimal control is used to ...

In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the...

1 We present efficient partial differential equation (PDE) methods for continuous time mean2 variance portfolio allocation problems when the underlying risky asset follows a stochastic 3 volatility process. The standard formulation for mean variance optimal portfolio allocation 4 problems gives rise to a two-dimensional non-linear Hamilton-Jacobi-Bellman (HJB) PDE. We 5 use a wide stencil metho...

We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice Z. Let T (x) be the first-passage time from the origin to a point x in Z. The convergence of the scaled first-passage time T ([nx])/n to the time-constant as n → ∞ can be viewed as a problem of homogenization for a discrete Hamilton-Jacobi-Bellman (HJB) equation. We derive an exact variational ...

We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, is constructed as a stochastic game two players: decision maker (DM) chooses “best” policy, and adverse player “worst” probability measure. The main result establishing optimal strategy (also referred to control) of DM showing it threshold policy. payoff are obtained by solving...

Abstract In this paper, we consider the stochastic optimal control problem for jump-diffusion models with state constraints. general, value function of such problems is discontinuous viscosity solution associated Hamilton-Jacobi-Bellman (HJB) equation since regularity cannot be guaranteed at boundary constraint. By adapting target theory, obtain an equivalent representation original by means ba...

We develop a discrete analogue of the Hamilton–Jacobi theory in the framework of the discrete Hamiltonian mechanics. We first reinterpret the discrete Hamilton–Jacobi equation derived by Elnatanov and Schiff in the language of discrete mechanics. The resulting discrete Hamilton– Jacobi equation is discrete only in time, and is shown to recover the Hamilton–Jacobi equation in the continuous-time...

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style an option price constructed as a difference certainty equivalents value functions solving HJB equations. We introduce transformation method for penalized nonlinear partial differential equation. transformed equation involves possibly non-constant risk aversi...