Extended weak convergence and utility maximisation with proportional transaction costs

Erhan Bayraktar, Leonid Dolinskyi () and Yan Dolinsky ()
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Leonid Dolinskyi: The University of the State Fiscal Service
Yan Dolinsky: Hebrew University

Finance and Stochastics, 2020, vol. 24, issue 4, No 6, 1013-1034

Abstract: 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).

Keywords: Utility maximisation; Proportional transaction costs; Extended weak convergence; Meyer–Zheng topology; 91B16; 91G10; 60F05 (search for similar items in EconPapers)
JEL-codes: C65 G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-020-00437-0

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