Time Consistency of the Mean-Risk Problem
Time Consistency of the Mean-Risk Problem
复制标题
平均风险问题的时间一致性
DOI：
10.1287/opre.2020.2002
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Birgit Rudloff
中科院分区：
文献类型：
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作者：
Gabriela Kováčová;Birgit Rudloff
在处理动态优化问题时，时间一致性是一个理想的属性，因为它允许人们通过向后递归有效地解决问题。平均风险问题是已知的时间不一致时，考虑在其标量形式。然而，当保持其原始的双目标形式时，它满足更一般的时间一致性属性，似乎更适合于向量优化问题。在“平均风险问题的时间一致性”中，Kováova和Rudloff引入了著名的贝尔曼原理的集值版本，并证明了双目标平均风险问题确实满足它。然后，上像，一个在其边界上包含有效边界的集合，在时间上向后递归。Kováova和Rudloff提出的条件下，这种递归可以直接利用动态规划的精神来计算解决方案。这为数学中的一个新的分支打开了大门：动态多元规划。
When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through a backward recursion. The mean-risk problem is known to be time inconsistent when considered in its scalarized form. However, when left in its original bi-objective form, it turns out to satisfy a more general time consistency property that seems better suited to a vector optimization problem. In “Time Consistency of the Mean-Risk Problem,” Kováĉova and Rudloff introduce a set-valued version of the famous Bellman principle and show that the bi-objective mean-risk problem does satisfy it. Then, the upper image, a set that contains the efficient frontier on its boundary, recurses backward in time. Kováĉova and Rudloff present conditions under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. This opens the door for a new branch in mathematics: dynamic multivariate programming.