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Hidden Markov Chain Filtering for Generalised Bessel Processes

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Abstract

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.

Suggested Citation

  • Robert Elliott & Eckhard Platen, 1999. "Hidden Markov Chain Filtering for Generalised Bessel Processes," Research Paper Series 23, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:23
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    References listed on IDEAS

    as
    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. Dembo, A. & Zeitouni, O., 1986. "Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 91-113, October.
    4. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    5. G. N. Milstein & Eckhard Platen & H. Schurz, 1998. "Balanced Implicit Methods for Stiff Stochastic Systems," Published Paper Series 1998-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.

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