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We address the problem of strategic asset allocation (SAA) with portfolios that include illiquid alternative asset classes. The main challenge in portfolio construction with illiquid asset classes is that we do not have direct control over our positions, as we do in liquid asset classes. Instead we can only make commitments; the position builds up over time as capital calls come in, and reduces over time as distributions occur, neither of which the investor has direct control over. The effect on positions of our commitments is subject to a delay, typically of a few years, and is also unknown or stochastic. A further challenge is the requirement that we can meet the capital calls, with very high probability, with our liquid assets. We formulate the illiquid dynamics as a random linear system, and propose a convex optimization based model predictive control (MPC) policy for allocating liquid assets and making new illiquid commitments in each period. Despite the challenges of time delay and uncertainty, we show that this policy attains performance surprisingly close to a fictional setting where we pretend the illiquid asset classes are completely liquid, and we can arbitrarily and immediately adjust our positions. In this paper we focus on the growth problem, with no external liabilities or income, but the method is readily extended to handle this case.