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).

中文翻译：

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扩展的弱收敛和效用最大化，交易成本成比例

在本文中，我们研究了具有成比例交易成本的效用最大化。假设基础过程的扩展弱收敛，我们证明了相应效用最大化问题的时间零值的收敛。此外，我们为最优交易策略建立了一个极限定理。证明基于Aldous（1981年在Strasbourg Manner中观察到的过程的随机过程的弱收敛）的扩展弱收敛理论以及在Meyer和Zheng（Ann。Inst。HenriPoincaréProbab）中引入的Meyer-Zheng拓扑。 Stat。20：353-372，1984）。