论文标题
优先鲁棒修改的优化确定性当量
Preference Robust Modified Optimized Certainty Equivalent
论文作者
论文摘要
Ben-Tal和Teboulle \ cite {Btt86}介绍了不确定结果的优化确定性（OCE）的概念，这是从目前的不确定收入中获得的现金组合的最大现值，以及剩余不确定收入的预期效用价值。在本文中，我们考虑了OCE的两种变体。首先，我们通过最大化现金效用和剩余不确定收入的预期效用的结合来介绍修改后的OCE，从而使合并数量的效用为统一的效用价值。其次，我们考虑了一个真正的效用函数未知的情况，但是可以使用部分可用的信息来构建一组合理的效用函数。为了减轻歧义引起的风险，我们引入了一个强大的模型，其中修改的OCE基于歧义集的最差案例效用函数。在以标称效用函数为中心的kantorovich球构造的效用函数的歧义集时，我们可以通过求解两个线性程序来显示修改后的OCE和相应的最坏情况效用函数。我们还显示，在数据驱动的环境中，强大的修改OCE在统计学上具有稳定性，其中潜在的数据可能被污染。据报道，一些初步的数值结果证明了修改后的OCE的性能和强大的修改OCE模型。
Ben-Tal and Teboulle \cite{BTT86} introduce the concept of optimized certainty equivalent (OCE) of an uncertain outcome as the maximum present value of a combination of the cash to be taken out from the uncertain income at present and the expected utility value of the remaining uncertain income. In this paper, we consider two variations of the OCE. First, we introduce a modified OCE by maximizing the combination of the utility of the cash and the expected utility of the remaining uncertain income so that the combined quantity is in a unified utility value. Second, we consider a situation where the true utility function is unknown but it is possible to use partially available information to construct a set of plausible utility functions. To mitigate the risk arising from the ambiguity, we introduce a robust model where the modified OCE is based on the worst-case utility function from the ambiguity set. In the case when the ambiguity set of utility functions is constructed by a Kantorovich ball centered at a nominal utility function, we show how the modified OCE and the corresponding worst case utility function can be identified by solving two linear programs alternatively. We also show the robust modified OCE is statistically robust in a data-driven environment where the underlying data are potentially contaminated. Some preliminary numerical results are reported to demonstrate the performance of the modified OCE and the robust modified OCE model.
