Sequential Tracking of a Hidden Markov Chain Using Point Process Observations

Details Sequential Tracking of a Hidden Markov Chain Using Point Process Observations Sequential Tracking of a Hidden Markov Chain Using Point Process Observations

2007-12-04

arxiv.org/abs/0712.0413v2

Mathematics

Optimization and Control

Key words and phrases. Markov Modulated Poisson processes, optimal switching

Scientific paper

We study finite horizon optimal switching problems for hidden Markov chain models under partially observable Poisson processes. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state variable using Bayesian updates over the discrete observations. Such a model has applications in economic policy making, staffing under variable demand levels and generalized Poisson disorder problems. We show regularity of the value function and explicitly characterize an optimal strategy. We also provide an efficient numerical scheme and illustrate our results with several computational examples.

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