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 assetand asymmetrical information. There are threefinancial agents: the market maker, an insider trader (who knows a randomvariable V which will be revealed at final time) and a non informed agent. Here we assume thatthe 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 ruleand to prove the existenceof an equilibrium price when the insider trader and the non informedagent 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.
