Monoyios, Michael (2010) *Optimal investment with inside information and parameter uncertainty.* Mathematics and Financial Economics, 3 . pp. 13-38.

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## Abstract

An optimal investment problem is solved for an insider who has access to noisy information related to a future stock price, but who does not know the stock price drift. The drift is filtered from a combination of price observations and the privileged information, fusing a partial information scenario with enlargement of filtration techniques. We apply a variant of the Kalman-Bucy filter to infer a signal, given a combination of an observation process and some additional information. This converts the combined partial and inside information model to a full information model, and the associated investment problem for HARA utility is explicitly solved via duality methods. We consider the cases in which the agent has information on

the terminal value of the Brownian motion driving the stock, and on the terminal stock price itself. Comparisons are drawn with the classical partial information case without insider knowledge. The parameter uncertainty results in stock price inside information being more valuable than Brownian information, and perfect knowledge of the future stock price leads to infinite additional utility. This is in contrast to the conventional case in which the stock drift is assumed known, in which perfect information of any kind leads to unbounded additional utility, since stock price information is then indistinguishable from Brownian information.

Item Type: | Article |
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Subjects: | O - Z > Probability theory and stochastic processes |

Research Groups: | Mathematical and Computational Finance Group |

ID Code: | 970 |

Deposited By: | Michael Monoyios |

Deposited On: | 16 Sep 2010 07:52 |

Last Modified: | 16 Sep 2010 07:52 |

### Available Versions of this Item

- Optimal investment with inside information and parameter uncertainty. (deposited 23 Mar 2010 07:48)
- Optimal investment with inside information and parameter uncertainty. (deposited 16 Sep 2010 07:52)
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- Optimal investment with inside information and parameter uncertainty. (deposited 16 Sep 2010 07:52)

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