A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

The existence of a linear equilibrium in Kyle’s model of market making with multiple, symmetrically informed strategic traders is implied for any number of strategic traders if the joint distribution of the underlying exogenous random variables is elliptical. The reverse implication has been shown for the case in which the random variables are independent and have finite second moments. Here we extend this result to the case in which the underlying random variables are not necessarily independent and their joint distribution is determined by its moments.