Optimal Portfolios with Proportional Transaction Costs and Stability

Summary

This note studies utility maximization when trading incurs proportional transaction costs. Its central aim is to prove a limit theorem for optimal trading strategies in that setting, addressing an open question identified by the authors. The result concerns how optimal strategies behave under the stated transaction-cost model, making the work relevant to portfolio optimization where trading frictions affect decisions.

The proof relies on establishing uniqueness of the optimal strategy, using a dual approach developed in earlier work. The supplied description does not state the theorem’s precise assumptions, the form of the limit, or any empirical evaluation. It is therefore a theoretical contribution about strategy stability, rather than evidence that a particular portfolio rule performs well in real markets.

Key ideas

• The note considers utility maximization with proportional trading costs.
• It establishes a limit theorem for optimal strategies and addresses an open question.
• The proof depends on proving uniqueness of the optimal strategy.
• A dual method provides the basis for the uniqueness argument.
• The description gives no empirical results or detailed theorem assumptions.

Tags

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


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









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

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.