Sequential tracking of a hidden Markov chain using point process observations |
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Authors: | Erhan Bayraktar Michael Ludkovski |
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Institution: | 1. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States;2. Department of Statistics and Applied Probability, University of California at Santa Barbara, CA 93106, United States |
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Abstract: | We study finite horizon optimal switching problems for hidden Markov chain models with point process observations. 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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Keywords: | primary 62L10 secondary 62L15 62C10 60G40 |
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