In this paper, we treat an optimal control problem of a stochastic two-machine owshop with machines subject to random breakdown and repair. While the problem is diicult to solve, it can be approximated by a deterministic problem when the rates of machine failure and repair become large. Furthermore, beginning with the solution of the deterministic problem, we can construct a feedback control fo...

Studies of dynamic economic models often rely on each agent having a smooth value function and a well-defined optimal strategy. For time-homogeneous optimal control problems with a one-dimensional diffusion, we prove that the corresponding value function must be twice continuously differentiable under Lipschitz, growth, and non-vanishing-volatility conditions. Under similar conditions, the valu...

An optimal stochastic control problem is considered for systems with unbounded controls satisfying an integral constraint. It is shown that there exists an optimal control within the class of generalized controls leading to impulse actions. Applying an approach of time transformation, developed recently for deterministic systems, the original control problem is shown to be equivalent to an opti...

We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the many-server heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponenti...

In this paper we consider the problem of constructing T -optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions. In general, the T -optimal discriminating design depends in a complicated way on the parameters of the la...

The jump diffusion process has come to play an important role in many branches of science and industry. In their book [25], Øksendal and Sulem have studied the optimal control, optimal stopping and impulse control for jump diffusion processes. In mathematical finance theory, many researchers have developed option pricing theory, for example, Merton [24] was the first to use the jump process to ...

We consider the problem of a seller who faces an unknown number of offers where each offer is a random draw from a known distribution. The objective of the seller is to maximize the probability that the highest offer is chosen. This is equivalent to maximizing expected utility when one assigns preferences to rankings of offers. We identify the optimal selling strategy using the technique of Por...

The paper describes the analysis, design and control of two new versions of spherical permanent magnet motor, which are capable of two and three degrees-of-freedom of controlled motion, and have a high specific torque capability. Their magnetic field distribution is established using an analytical technique formulated in spherical coordinates. This enables the torque vector and back-emf to be d...

The problem of Optimal Stopping is of fundamental importance for sequential analysis, for the detection of signals in a background of noise, and also for pricing American-type options in the modern theory of finance. We shall review in this talk two relatively recent approaches to this problem: the deterministic or “pathwise” approach of Davis & Karatzas (1994), and the “integral representation...