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.

Zugehörige Institution(en) am KIT |
Institut für Stochastik (STOCH) |

Publikationstyp |
Zeitschriftenaufsatz |

Jahr |
2005 |

Sprache |
Englisch |

Identifikator |
DOI: 10.1239/jap/1118777176 ISSN: 0021-9002 URN: urn:nbn:de:swb:90-436167 KITopen ID: 1000043616 |

Erschienen in |
Journal of Applied Probability |

Band |
42 |

Heft |
2 |

Seiten |
362-378 |

Schlagworte |
portfolio optimization, Markov-modulated drift, HJB equation, optimal investment strategies, Bayesian control, stochastic orderings |

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