Abstract
In this paper we propose a type of mean reverting model with jumps, where the mean reverting level changes according to a continuous time, finite state Markov chain. This model could be applied to the interest rate and energy markets. We apply filtering techniques and obtain finite dimensional filters for the unobservable state of the Markov chain based on observations of the mean reverting diffusion. Various auxiliary filters are developed that allow us to estimate the parameters of the Markov chain by the EM algorithm. A simulation study is done for a concrete example.
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