In this note we formulate an optimality problem for Stochastic process with a regime absorbing state. We present a solution for this problem as a pair of differential equations that are recusrsively linked. As an application I obtain an analytical for the Merton portfolio problem in a case for a...

This paper presents an asymptotic analysis of control models governed by stochastic ordinary differential equations. A sufficient condition of near-optimal controls is given based on Ekeland's principle. It is shown that, under some concavity assumptions, the e-maximum condition in terms of the...

We consider the instantaneous control of a diffusion process on the real line. Two types of costs are incurred: the holding and transaction costs. The holding cost is incurred at all times at the rate modeled by a convex function of the state. Transactions costs have both a fixed component and a...

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling...

A fundamental alternative for stochastic optimization problems named focus programming is proposed based on the focus theory of choice. Different from the existing approaches such as chance-constrained programming and two-stage stochastic programming which are based on expected utility theory,...