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

§Dedicated to the memory of Axel Grorud.

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.

Keywords:

• Forward integral
• Malliavin derivative
• Insider trading
• Utility function
• Enlargement of filtration

Acknowledgments

We thank Francesca Biagini for helpful comments and suggestions.

Notes

§Dedicated to the memory of Axel Grorud.