Quadratic hedging in an incomplete market derived by an influential informed investor

Abstract

This paper presents a model with an influential and informed investor. A hedging problem is studied from the point of view of a non-informed agent in an influenced and informed market. Her lack of information makes the market incomplete. Obtained results, by means of Malliavin calculus and Clark–Ocone formula, as well as filtering theory, are the expressions and a comparison between the strategy of the non-informed trader and the strategy of the informed agent. An expression of the residual risk a non-informed trader keeps by detaining an option in this influenced and informed market is derived using a quadratic approach of hedging in incomplete market. Finally, the analysis leads to a measure of the lack of information that makes the market incomplete. The financial interpretation is explained throughout the theoretical analysis, together with an example of such influenced informed model.