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Abstract
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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 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.
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