This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the duality approach. As an important application of the duality theorem, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form similar to Czichowsky and Schachermayer (Ann Appl Probab 26(3):1888–1941, 2016) as well as in the usual sense using acceptable portfolios.

中文翻译：

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具有随机end赋和交易成本的最优投资：对偶理论和影子价格

本文研究了具有随机end赋和成比例交易成本的终端财富的效用最大化。为了处理一些流动性差的债权的无限制随机收益，我们建议使用通过一致的价格系统定义的可接受的投资组合，以使清算价值过程保持在某些随机阈值之上。在由一种无风险债券和一种风险资产组成的市场中，我们获得了一种超级对冲结果。基于对原始空间的这种刻画，利用对偶方法建立了效用最大化问题最优解的存在性和唯一性。作为对偶定理的重要应用，