This paper studies the problem of optimal investment in incomplete markets,
robust with respect to stopping times. We work on a Brownian motion framework
and the stopping times are adapted to the Brownian filtration. Robustness can
only be achieved for logartihmic utility, otherwise a cashflow should be added
to the investor s wealth. The cashflow can be decomposed into the sum of an
increasing and a decreasing process. The last one can be viewed as consumption.
The first one is an insurance premium the agent has to pay.