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Signal-to-noise matrix and model reduction in continuous-time hidden Markov models

Author

Listed:
  • Elisabeth Leoff

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Leonie Ruderer
  • Jörn Sass

    (Technische Universität Kaiserslautern)

Abstract

Continuous-time regime-switching models are a very popular class of models for financial applications. In this work the so-called signal-to-noise matrix is introduced for hidden Markov models where the switching is driven by an unobservable Markov chain. Its relations to filtering, i.e. state estimation of the chain given the available observations, and portfolio optimization are investigated. A convergence result for the filter is derived: The filter converges to its invariant distribution if the eigenvalues of the signal-to-noise matrix converge to zero. This matrix is then also used to prove a mutual fund representation for regime-switching models and a corresponding market reduction which is consistent with filtering and portfolio optimization. Two canonical cases for the reduction are analyzed in more detail, the first based on the market regimes and the second depending on the eigenvalues. These considerations are presented both for observable and unobservable Markov chains. The results are illustrated by numerical simulations.

Suggested Citation

  • Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.
    • Handle: RePEc:spr:mathme:v:95:y:2022:i:2:d:10.1007_s00186-022-00784-y
    DOI: 10.1007/s00186-022-00784-y
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