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).
Bibliographical noteFunding Information:
E. Bayraktar is supported in part by the National Science Foundation under grant DMS-1613170 and in part by the Susan M. Smith Professorship. Y. Dolinsky is supported in part by the GIF Grant 1489-304.6/2019 and the ISF grant 160/17.
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- Extended weak convergence
- Meyer–Zheng topology
- Proportional transaction costs
- Utility maximisation