The Numéraire Property and Long-term Growth Optimality for Drawdown-constrained Investments

We consider the portfolio choice problem for an investor interested in long-run growth optimality while facing drawdown constraints in a general continuous semimartingale model. The paper introduces the numéraire property through the notion of expected relative return and shows that drawdown-constrained strategies with the numéraire property exist and are unique, but may depend on the financial planning horizon. We explicitly characterize the growth-optimal strategy and show that it enjoys the numéraire property within the class of investments satisfying the drawdown constraint, when sampled at the times of its maximum and asymptotically as the timehorizon becomes distant. Finally, it is established that the asymptotically growth-optimal strategy is obtained as limit of numéraire strategies on finite horizons.