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Quantitative Finance Volume 6, 2006 - Issue 1
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Original Articles

Optimal portfolio for an insider in a market driven by Lévy processesFootnote§

Giulia Di Nunno Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, NorwayCorrespondence[email protected]
,
Thilo Meyer-Brandis Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway
,
Bernt Øksendal Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway; Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway
&
Frank Proske Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway
Pages 83-94 | Received 25 Feb 2005, Accepted 02 Nov 2005, Published online: 18 Feb 2007
 
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Abstract

We consider a financial market driven by a Lévy process with filtration . An insider in this market is an agent who has access to more information than an honest trader. Mathematically, this is modelled by allowing a strategy of an insider to be adapted to a bigger filtration . The corresponding anticipating stochastic differential equation of the wealth is interpreted in the sense of forward integrals. In this framework, we study the optimal portfolio problem of an insider with logarithmic utility function. Explicit results are given in the case where the jumps are generated by a Poisson process.

§Dedicated to the memory of Axel Grorud.

Acknowledgments

We thank Francesca Biagini for helpful comments and suggestions.

Notes

§Dedicated to the memory of Axel Grorud.

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