Skip to content
All library documents

Convergence of Utility-Optimal Trading with Proportional Costs

Article arXiv papers · Author: Erhan Bayraktar et al.
Read the original

Summary

This paper studies utility maximization when trading incurs proportional transaction costs. Its central result is that, under an assumption of extended weak convergence for the underlying processes, the associated utility maximization problems converge as well. It also establishes a limit theorem for the optimal trading strategies, addressing how strategies in the approximating problems relate to those in the limiting problem.

The proofs draw on extended weak convergence theory and the Meyer–Zheng topology. These are mathematical tools for handling convergence of stochastic processes and their associated optimization problems. The document provides theorem-level results rather than a numerical example, practical strategy, or empirical trading test. Its conclusions are conditional on the stated convergence framework; the brief description does not specify the market model, utility function, exact assumptions, or how the results might guide implementation under real execution constraints.

Key ideas

  • The paper analyzes utility maximization with proportional transaction costs.
  • Extended weak convergence of the underlying processes yields convergence of the optimization problems.
  • A limit theorem connects optimal strategies across the approximating and limiting problems.
  • The proofs use extended weak convergence theory and the Meyer–Zheng topology.
  • The document gives mathematical results but no empirical assessment or implementation example.

Tags

StatisticsRisk managementExecutionPortfolio construction
Full text
# Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs


# Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs









In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in [1] and the Meyer--Zheng topology introduced in [24].

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.