A general stochastic calculus approach to insider trading

Abstract

The purpose of this paper is to present a general stochastic calculus approach to insider trading. In a market driven by a standard Brownian motion B(t) on a filtered probability space (Ω, F, {F}t>0, P), by an insider we mean a person who has access to a filtration (information) G = {Gt}0≤t≤T which is strictly bigger than the filtration F = {Ft}0≤t≤T of B(t). In this context an insider strategy is represented by a Gt-adapted process φ(t) and we interpret the portfolio of an insider as the forward integral

defined in [18].

We consider an optimal portfolio problem with logarithmic utility for an insider with access to general information Gt Ft and show that if the value of this problem is finite and an optimal insider portfolio π*(t) exists, then Bt is a Gt-semimartingale, i.e. the enlargement of filtration property holds. This is a partial converse of previously known results in this field.