  We study the portfolio selection problem of a long-run investor who is
maximising the asymptotic growth rate of her expected utility. We show that,
somewhat surprisingly, it is essentially not affected by introduction of a
floor constraint which requires the wealth process to dominate a given
benchmark at all times. We further study the notion of long-run optimality of
wealth processes via convergence of finite horizon value functions to the
asymptotic optimal value. We characterise long-run optimality under floor and
drawdown constraints.
