## Team : mathfi

## Section: New Results

**Keywords: ***antipative calculus*, *forward integrals*, *insider*, *asymmetry information*.

## Utility maximization in an insider influenced market

**Participants:**A. Kohatsu Higa, A. Sulem.

We study a controlled stochastic system whose state is described by a stochastic differential equation where the coefficients are anticipating. This setting is used to interpret markets where insiders have some influence on the dynamics of prices.This point of view was already partly studied in Øksendal-Sulem [47] although the financial consequences and modelling possibilities for models of markets with insiders were not exploited there. We give a characterization theorem for the optimal logarithmic portfolio of an investor with a different information flow from that of the insider. As examples, we provide explicit results in the partial information case which we extend in order to incorporate the enlargement of filtration techniques for markets with insiders.

Finally, we consider a market with an insider which influences the drift of the asset process. This last example, which does not seem to fit into the enlargement of filtration set-up, gives a situation where it makes a difference for a small agent to acknowledge the existence of the insider in the market [23].