  We assume that an individual invests in a financial market with one riskless
and one risky asset, with the latter's price following geometric Brownian
motion as in the Black-Scholes model. Under a constant rate of consumption, we
find the optimal investment strategy for the individual who wishes to minimize
the probability that her wealth drops below some fixed proportion of her
maximum wealth to date, the so-called probability of {\it lifetime drawdown}.
If maximum wealth is less than a particular value, $m^*$, then the individual
optimally invests in such a way that maximum wealth never increases above its
current value. By contrast, if maximum wealth is greater than $m^*$ but less
than the safe level, then the individual optimally allows the maximum to
increase to the safe level.
