Section: New Results
Keywords : anticipative calculus, forward integrals, insider, asymmetry information.
Utility maximization in an insider influenced market
In  , A. Kohatsu Higa and A. Sulem have studied 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. An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market. In  , A. Kohatsu Higa and A. Sulem give some remarks on the anticipating approach to insider modeling introduced by the authors recently. In particular, they define forward integrals by using limits of Riemmann sums. This definition is well adapted to financial applications. As an application, they consider a portfolio maximization problem of a large trader with insider information. They show that the forward integral is a natural tool to handle such problems and compute the optimal portfolios for an insider and a small trader.
In a joint work with mathematicians from the university of Oslo, A. Kohatsu Higa and A. Sulem consider in  the optimization problem of an insider who is so influential in the market to affect the price dynamics: in this sense he is called a ``large'' insider. The optimal portfolio problem for a general utility function is studied for a financial market driven by a Lévy process in the framework of forward anticipating calculus.