Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach

Research paper by Jan Kallsen, Shen Li

Indexed on: 13 Sep '13Published on: 13 Sep '13Published in: arXiv - Quantitative Finance - Portfolio Management


We consider an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In the present paper, we carry out a convex duality approach facilitated by the concept of shadow price processes in order to verify the main results of Kallsen and Muhle-Karbe under well-defined regularity conditions.