We tackle portfolio optimization problems in the presence of proportional transaction costs by determining a shadow price, which is a solution to the dual problem. That is, it is a fictitious frictionless price process evolving within the bid-ask spread of the original market with transaction costs, such that the optimal trading strategies in both markets coincide. For small transaction costs, we show how to represent the relevant quantities as power series, whose coefficients can be algorithmically computed in closed form up to arbitrary order.
Keywords: Transaction costs; Portfolio optimization; Shadow price; Asymptotics
Biography: Johannes Muhle-Karbe received his Ph.D., supervised by Jan Kallsen, from TU München in 2009. Afterwards, he spent a year in Vienna as a PostDoc in Walter Schachermayer's group. Since October 2010, he is an assistant professor for mathematical finance at ETH Zürich.