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 numeraire property through the notion of expected relative return and shows that drawdown-constrained strategies with the numeraire 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 numeraire property within the class of investments satisfying the drawdown constraint , when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant . Finally , it is established that the asymptotically growth-optimal strategy is obtained as limit of numeraire strategies on finite horizons.
We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We suggest to use path-wise growth optimality as the decision criterion and encode preferences through restrictions on the class of admissible wealth processes. Specifically, the investor is only interested in strategies which satisfy a given linear drawdown constraint. The paper introduces the numeraire property through the notion of expected relative return and shows that drawdown-constrained strategies with the numeraire property exist and are unique, but may depend on the financial planning horizon. However , when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant , the drawdown-constrained numeraire portfolio is given explicitly through a model-independent transformation of the unconstrained numeraire portfolio. Further , it is established that the asymptotically growth-optimal strategy is obtained as limit of numeraire strategies on finite horizons.
D
an investor interested in long-run growth optimality while facing drawdown constraints in
A
long-run investor in a
A
We suggest to use path-wise growth optimality as the decision criterion and encode preferences through restrictions on the class of admissible wealth processes. Specifically, the investor is only interested in strategies which satisfy a given linear drawdown constraint.
R
We explicitly characterize the growth-optimal strategy and show that it enjoys the numeraire property within the class of investments satisfying the drawdown constraint
However
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. Finally
, the drawdown-constrained numeraire portfolio is given explicitly through a model-independent transformation of the unconstrained numeraire portfolio. Further