Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.