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

Optimal portfolios of a long-term investor with floor or drawdown constraints