Abstract
To solve utility maximization problems under proportional transaction costs, one can sometimes replace the original market with transaction costs by a frictionless shadow market that gives the same optimal strategy and utility. In this talk we provide sufficient conditions, when this is possible, as well as counter-examples in the case the conditions are not satisfied. For the geometric Ornstein-Uhlenbeck process we explicitly construct such a shadow price to determine the growth-optimal portfolio under transaction costs and explain the effects resulting from the stochastic investment opportunity set in this construction. The talk is based on joint work(s) with Philipp Deutsch, Johannes Muhle-Karbe and Walter Schachermayer.