Hidden Markov Chain Filtering for a Jump Diffusion Model

Abstract

In this paper, we derive the finite-dimensional recursive filters for a jump diffusion model with a drift parameter that follows hidden Markov chains. These finite-dimensional filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model and the jump intensity rate.

Key Words:

• Filtering equations
• Martingale
• Reference probability

Mathematics Subject Classification:

• 93E11
• 92B28

ACKNOWLEDGMENTS

This research was supported by the Natural Science and Engineering Research Council of Canada and Mathematics of Information Technology and Complex Systems, Canada. Ping Wu wants to express his thanks to Professor S. Feng and Professor T. Hurd for their assistance.