  We study the problem of optimal portfolio selection in an illiquid market
with discrete order flow. In this market, bids and offers are not available at
any time but trading occurs more frequently near a terminal horizon. The
investor can observe and trade the risky asset only at exogenous random times
corresponding to the order flow given by an inhomogenous Poisson process. By
using a direct dynamic programming approach, we first derive and solve the
fixed point dynamic programming equation satisfied by the value function, and
then perform a verification argument which provides the existence and
characterization of optimal trading strategies. We prove the convergence of the
optimal performance, when the deterministic intensity of the order flow
approaches infinity at any time, to the optimal expected utility for an
investor trading continuously in a perfectly liquid market model with no-short
sale constraints.
