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Hidden Markov Chain Filtering for Generalised Bessel Processes

Finite-dimensional recursive filters are obtained for generalised Bessel processes with a drift parameter that follows a hidden Markov chain. In particular, filters are constructed for the states, the jumps and the occupation times of the states of the Markov chain. These lead to estimators for the transition rates and the levels of the hidden states of the chain. Finally a minimum variance filter is described that minimises fluctuations of the filters.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 23.

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Date of creation: 01 Dec 1999
Date of revision:
Publication status: Published as: Elliott, R. and Platen, E., 2001, "Hidden Markov Chain Filtering for Generalised Bessel Processes", Stochastics in Finite and Infinite Dimensions: Trends in Mathematics, 123-143.
Handle: RePEc:uts:rpaper:23
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  1. Fischer Paul & Platen Eckhard, 1999. "Applications of the balanced method to stochastic differential equations in filtering," Monte Carlo Methods and Applications, De Gruyter, vol. 5(1), pages 19-38, December.
  2. Eckhard Platen, 1999. "A Minimal Share Market Model with Stochastic Volatility," Research Paper Series 21, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
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