A general stochastic calculus approach to insider trading

The purpose of this paper is to present a general stochastic calculus approach to insider trading. We consider a market driven by a standard Brownian motion B(t) on a filtered probability space. By an insider in this market we mean a person who has access to a filtration H (information) which is strictly bigger than the filtration F of the Brownian motion. In this context an insider strategy is represented by an H-adapted process and we interpret all anticipating integrals as the forward integral. We consider an optimal portfolio problem with general utility for an insider with access to a general information and show that if an optimal insider portfolio of this problem exists, then B(t) is an H-semimartingale, i.e. the enlargement of filtration property holds. This is a converse of previously known results in this field. Moreover, if an optimal solution exists we obtain an explicit expression in terms of it for the semimartingale decomposition of B(t) with respect to H.