Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309542 
Year of Publication: 
2022
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 95 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 327-359
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Hidden Markov model
Mutual fund
Portfolio optimization
Regime switching
Stochastic filtering
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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