Controlled diffusion processes

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Effects of Implementation Delay on Decision-Making Under Uncertainty

In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its counterparts that use quasi-variational inequalities. Our method is direct, in the sense that we do not have to guess the form of the solution and we do not have to prove that the conjectured solution satisfies conditions of a verification lemma. Second, by employing this direct solution method, we solve two examples that involve decision delays: an exchange rate intervention problem and a problem of labor force optimization

An irreversible investment model with a stochastic production capacity and fixed plus proportional adjustment costs

This paper studies the problem of a company which expands its stochastic production capacity in irreversible investments by purchasing capital and faces both fixed and proportional costs. The objective of the company is to find optimal production decisions to maximize its expected total net profit in an infinite horizon. We solve this problem explicitly by applying the theory of stochastic impulse controls.Irreversible investment; production; quasi-variational inequalities; stochastic impulse control