Weak Kyle-Back Equilibrium Models for Max and ArgMax

The goal of this article is to introduce a new approach to model equilibrium in financial markets with an insider. We prove the existence and uniqueness in law of equilibrium for these markets. Our setting is weaker than Back’s one and it can be interpreted as a first theoretical step towards developing statistical test procedures. Additionally, it allows various forms of insider information to be considered under the same framework and compared. As major examples, we consider the cases of the maximum of the demand and the time at which this maximum is taken, which have not been previously treated in the literature of equilibrium in financial markets with inside information. Simulations indicate that the expected wealth for the maximum is greater than the expected wealth for its argument.