We consider an extension of the Kyle and Back's model [Back, Rev. Finance Stud.5 (1992) 387–409; Kyle, Econometrica35 (1985) 1315–1335],
meaning a model for the market with a continuous time risky asset
and asymmetrical information. There are three
financial agents: the market maker, an insider trader (who knows a random
variable V which will be revealed at final time) and a non informed
agent. Here we assume that
the non informed agent is strategic, namely he/she uses a utility
function to optimize his/her strategy.
Optimal control theory is applied to obtain a pricing rule
and to prove the existence
of an equilibrium price when the insider trader and the non informed
agent are risk-neutral. We will show that if such an equilibrium exists,
then the non informed agent's optimal strategy is to do nothing, in other
words to be non strategic.