  In this paper we show how the relaxation techniques can be used to establish
the existence of an optimal contract in presence of information asymmetry. The
method we illustrate was initially motivated by the problem of designing
optimal brokerage fees, but it does apply to other optimal contract problems,
in which (i) the agent controls linearly the drift of a diffusion process, (ii)
the direct dependence of the principal's and the agent's objectives on the
strategy of the agent is of a special form, and (iii) the space of admissible
contracts is compact. This method is then applied to establish existence of an
optimal brokerage fee in a market model with a private trading signal observed
by the broker's client but not by the broker.
