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

Anne Eyraud-Loisel (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

In this paper a model with an influent and informed investor is presented. The studied problem is the point of view of a non informed agent hedging an option in this influenced and informed market. Her lack of information makes the market incomplete to the non informed agent. The 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 incompleteness of the market. The financial interpretation is explained throughout the theoretical analysis, together with an example of such influenced informed model.

Mots clés: Clark-Ocone formula; influent investor; asymmetric information; Clark-Ocone formula.; martingale representation; Enlargement of filtration; FBSDE; quadratic hedging; risk minimization; insider trading

Domaines: Finance [q-fin.GN]; Probabilités [math.PR]

Anne Eyraud-Loisel. Quadratic hedging in an incomplete market derived by an influent informed investor. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, ⟨10.1080/17442508.2011.652632⟩. ⟨hal-00450949⟩