3:00 p.m., Friday (January 25, 2008)
Math Annex 1100
University of Michigan
Optimal Stopping and Optimal Switching for Hidden Markov Models
Abstract: We study optimal stopping and optimal switching problems for
hidden Markov chains with Poissonian information structures. In our
model, the controller maximizes expected rewards that depend on an
unobserved Markovian environment with information collected through a
(compound) Poisson observation process. Examples of such systems arise
in investment timing, reliability theory, sequential tracking, and
economic policy making. We solve the problem by performing Bayesian
updates of the posterior likelihoods of the unobservable and studying
the resulting optimization problem for a piecewise-deterministic
process. We then prove the dynamic programming principle and explicitly
characterize an optimal strategy. We also provide an efficient numerical
scheme and illustrate our results with several computational examples.
This is based on joint work with Semih Sezer and Erhan Bayraktar (U of M).
Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).