544 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
On the Solution of General Impulse Control Problems Using Superharmonic Functions
In this paper, a characterization of the solution of impulse control problems
in terms of superharmonic functions is given. In a general Markovian framework,
the value function of the impulse control problem is shown to be the minimal
function in a convex set of superharmonic functions. This characterization also
leads to optimal impulse control strategies and can be seen as the
corresponding characterization to the description of the value function for
optimal stopping problems as a smallest superharmonic majorant of the reward
function. The results are illustrated with examples from different fields,
including multiple stopping and optimal switching problems
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