  We consider a controlled diffusion process $(X_t)_{t\ge 0}$ where the
controller is allowed to choose the drift $\mu_t$ and the volatility $\sigma_t$
from a set $\K(x) \subset \R\times (0,\infty)$ when $X_t=x$. By choosing the
largest $\frac{\mu}{\sigma^2}$ at every point in time an extremal process is
constructed which is under suitable time changes stochastically larger than any
other admissible process. This observation immediately leads to a very simple
solution of problems where ruin or hitting probabilities have to be minimized.
Under further conditions this extremal process also minimizes "drawdown"
probabilities.

Probability;Portfolio Management