## A martingale method of portfolio optimization for unobservable mean rate of return

- In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.

Author: | Juri Hinz, Ralf Korn |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-10796 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (68) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2000 |

Year of Publication: | 2000 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2000/09/11 |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |