SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 494-525, January 2020.
We study an inverse investment problem proposed by Black and provide necessary and sufficient conditions for a given function to be an admissible indirect utility function in a log-normal market; we also show how to recover the associated utility function. Similar questions are also addressed starting directly from the initial investment choice. In parallel we study so-called forward investment-consumption criteria with the dynamic property that their volatility component is identically zero. We provide a fully forward characterization of such criteria and use it to construct forward preferences. We also provide explicit formulas for the associated optimal strategies and characterize the class of criteria which may be decomposed into a pure forward investment criterion and an infinite horizon Merton problem.

中文翻译：

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布莱克的逆投资问题和带消费的正向准则

SIAM金融数学杂志，第11卷，第2期，第494-525页，2020年1月。
我们研究了布莱克提出的逆向投资问题，并为给定函数成为对数正态市场上可接受的间接效用函数提供了充要条件。我们还将展示如何恢复相关的效用函数。直接从初始投资选择开始也解决了类似的问题。并行地，我们研究具有动态特性的所谓的远期投资-消费标准，它们的波动成分完全为零。我们提供了此类标准的全面前瞻性描述，并使用它来构建前瞻性偏好。我们还为相关的最佳策略提供了明确的公式，并描述了可分解为纯远期投资标准和无限水平默顿问题的标准类别。