  We study a continuous-time expected utility maximization problem in which the
investor at maturity receives the value of a contingent claim in addition to
the investment payoff from the financial market. The investor knows nothing
about the claim other than its probability distribution, hence an ``intractable
claim''. In view of the lack of necessary information about the claim, we
consider a robust formulation to maximize her utility in the worst scenario. We
apply the quantile formulation to solve the problem, expressing the quantile
function of the optimal terminal investment income as the solution of certain
variational inequalities of ordinary differential equations and obtaining the
resulting optimal trading strategy. In the case of an exponential utility, the
problem reduces to a (non-robust) rank--dependent utility maximization with
probability distortion whose solution is available in the literature. The
results can also be used to determine the utility indifference price of the
intractable claim.
