Extended weak convergence and utility maximisation with proportional transaction costs

Erhan Bayraktar; Leonid Dolinskyi; Yan Dolinsky

doi:10.1007/s00780-020-00437-0

Extended weak convergence and utility maximisation with proportional transaction costs

Erhan Bayraktar, Leonid Dolinskyi, Yan Dolinsky^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence of the time-0 values of the corresponding utility maximisation problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in Aldous (Weak Convergence of Stochastic Processes for Processes Viewed in the Strasbourg Manner, 1981) and on the Meyer–Zheng topology introduced in Meyer and Zheng (Ann. Inst. Henri Poincaré Probab. Stat. 20:353–372, 1984).

Original language	English
Pages (from-to)	1013-1034
Number of pages	22
Journal	Finance and Stochastics
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00780-020-00437-0
State	Published - 1 Oct 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Extended weak convergence
Meyer–Zheng topology
Proportional transaction costs
Utility maximisation

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10.1007/s00780-020-00437-0

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AU - Bayraktar, Erhan

AU - Dolinskyi, Leonid

AU - Dolinsky, Yan

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N2 - In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence of the time-0 values of the corresponding utility maximisation problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in Aldous (Weak Convergence of Stochastic Processes for Processes Viewed in the Strasbourg Manner, 1981) and on the Meyer–Zheng topology introduced in Meyer and Zheng (Ann. Inst. Henri Poincaré Probab. Stat. 20:353–372, 1984).

AB - In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence of the time-0 values of the corresponding utility maximisation problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in Aldous (Weak Convergence of Stochastic Processes for Processes Viewed in the Strasbourg Manner, 1981) and on the Meyer–Zheng topology introduced in Meyer and Zheng (Ann. Inst. Henri Poincaré Probab. Stat. 20:353–372, 1984).

KW - Extended weak convergence

KW - Meyer–Zheng topology

KW - Proportional transaction costs

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Extended weak convergence and utility maximisation with proportional transaction costs

Abstract

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Keywords

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