Theory of Probability &Its Applications, Volume 67, Issue 2, Page 229-245, August 2022.
This paper addresses the log-optimal portfolio, which is the portfolio with finite expected log-utility that maximizes the expected logarithm utility from terminal wealth, for an arbitrary general semimartingale model. The most advanced literature on this topic elaborates existence and characterization of this portfolio under the no-free-lunch-with-vanishing-risk (NFLVR for short) assumption, while there are many financial models violating NFLVR and admitting the log-optimal portfolio. In this paper, we provide a complete and explicit characterization of the log-optimal portfolio and its associated optimal deflator, give necessary and sufficient conditions for their existence, and elaborate their duality no matter what the market model. Furthermore, our characterization gives an explicit and direct relationship between log-optimal and numéraire portfolios without changing the probability or the numéraire.

中文翻译：

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没有 NFLVR 的对数最优投资组合：存在、完整表征和二元性

概率论及其应用，第 67 卷，第 2 期，第 229-245 页，2022 年 8 月。
本文讨论了对数最优投资组合，它是具有有限预期对数效用的投资组合，它使终端财富的预期对数效用最大化，用于任意一般半鞅模型。关于这个主题的最先进的文献详细阐述了在没有风险的无免费午餐（简称 NFLVR）假设下该投资组合的存在和表征，同时有许多金融模型违反 NFLVR 并承认对数最优投资组合。在本文中，我们提供了对数最优投资组合及其相关最优平减指数的完整和明确的表征，给出了它们存在的必要和充分条件，并阐述了它们在任何市场模型下的对偶性。此外，