927 research outputs found
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
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