  The folk result in Kyle-Back models states that the value function of the
insider remains unchanged when her admissible strategies are restricted to
absolutely continuous ones. In this paper we show that, for a large class of
pricing rules used in current literature, the value function of the insider can
be finite when her strategies are restricted to be absolutely continuous and
infinite when this restriction is not imposed. This implies that the folk
result doesn't hold for those pricing rules and that they are not consistent
with equilibrium. We derive the necessary conditions for a pricing rule to be
consistent with equilibrium and prove that, when a pricing rule satisfies these
necessary conditions, the insider's optimal strategy is absolutely continuous,
thus obtaining the classical result in a more general setting.
  This, furthermore, allows us to justify the standard assumption of absolute
continuity of insider's strategies since one can construct a pricing rule
satisfying the necessary conditions derived in the paper that yield the same
price process as the pricing rules employed in the modern literature when
insider's strategies are absolutely continuous.
