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Portfolio optimization with unobservable Markov-modulated drift process

Rieder, Ulrich; Bäuerle, Nicole ORCID iD icon


We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

Volltext §
DOI: 10.5445/IR/1000043616
DOI: 10.1239/jap/1118777176
Zitationen: 84
Web of Science
Zitationen: 81
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Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2005
Sprache Englisch
Identifikator ISSN: 0021-9002
KITopen-ID: 1000043616
Erschienen in Journal of Applied Probability
Verlag Applied Probability Trust
Band 42
Heft 2
Seiten 362-378
Schlagwörter portfolio optimization, Markov-modulated drift, HJB equation, optimal investment strategies, Bayesian control, stochastic orderings
Nachgewiesen in Scopus
Web of Science
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