On Robust Utility Maximization
arXiv:math/0702727
Abstract
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.