Time-Consistent Decisions and Temporal Decomposition of Coherent Risk Functionals
Time-Consistent Decisions and Temporal Decomposition of Coherent Risk Functionals
复制标题
时间一致的决策和相干风险泛函的时间分解
DOI：
--
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
A. Pichler
中科院分区：
文献类型：
--
作者：
G. Pflug;A. Pichler
在管理和规划中，随着时间的推移，额外的信息逐渐变得可用是司空见惯的。众所周知，大多数风险措施（风险泛函）在以下意义上是时间一致的：可能发生的是，在给定的时间段，某些损失分布看起来比另一个损失分布风险更小，但是在稍后的时间查看条件分布，本文引入的扩展条件风险泛函使初始风险的时间分解成为可能函数，可用于确保过去和未来偏好之间的一致性。中心的结果是一个分解定理，它允许重组的初始一致的风险功能复合的条件风险泛函，而不会丢失信息或偏好。从我们的研究结果可以看出，部分信息的及时披露，必须改变决策者的偏好，为一致性的原因，在其余的行动方案。此外，在许多情况下，扩展的条件风险泛函允许不同的政策，即使是基于不完全的information.Also的排名，我们使用的反例表明，没有改变的措施，唯一的时间一致的风险泛函的期望和本质上确界。
In management and planning it is commonplace for additional information to become available gradually over time. It is well known that most risk measures (risk functionals) are time in consistent in the following sense: it may happen that at a given time period, some loss distribution appears to be less risky than another one, but looking at the conditional distribution at a later time, the opposite relation holds almost surely.The extended conditional risk functionals introduced in this paper enable a temporal decomposition of the initial risk functional that can be used to ensure consistency between past and future preferences. The central result is a decomposition theorem, which allows recomposing the initial coherent risk functional by compounding the conditional risk functionals without losing information or preferences. It follows from our results that the revelation of partial information in time must change the decision maker’s preferences—for consistency reasons—among the remaining courses of action. Further, in many situations, the extended conditional risk functional allows ranking of different policies, even based on incomplete information.In addition, we use counterexamples to show that without change-of-measures, the only time-consistent risk functionals are the expectation and the essential supremum.