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The aim of this short note is to establish a limit theorem for the optimaltrading strategies in the setup of the utility maximization problem withproportional transaction costs. This limit theorem resolves the open questionfrom [4]. The main idea of our proof is to establish a uniqueness result forthe optimal strategy. The proof of the uniqueness is heavily based on the dualapproach which was developed recently in [6,7,8].

A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios