论文标题
部分可观测时空混沌系统的无模型预测
Randomization of Spectral Risk Measure and Distributional Robustness
论文作者
论文摘要
在本文中，我们考虑了一种情况，可以通过光谱风险措施（SRM）来描述决策者（DM）的风险偏好，但是没有一个SRM可以用来始终如一地表示DM的偏好。因此，我们建议通过在风险频谱中引入随机参数来随机化SRM。随机的SRM（RSRM）允许一个人描述不同SRM的不同状态的DM偏好。当已知随机参数的分布，即，可以通过概率分布来描述DM偏好的随机性时，我们引入了一种新的风险度量，即RSRM的平均值。在分布未知的情况下，我们提出了RSRM的分布鲁棒公式。 RSRM范式提供了一个新的框架，用于解释众所周知的Kusuoka代表不变的相干风险措施，并解决因观察/测量错误或偏好引发过程中错误响应而引起的不一致问题。我们详细讨论了基于RSRM和分布强大的RSRM解决优化问题的计算方案。
In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently. Consequently we propose to randomize the SRM by introducing a random parameter in the risk spectrum. The randomized SRM (RSRM) allows one to describe the DM's preferences at different states with different SRMs. When the distribution of the random parameter is known, i.e., the randomness of the DM's preference can be described by a probability distribution, we introduce a new risk measure which is the mean value of the RSRM. In the case when the distribution is unknown, we propose a distributionally robust formulation of RSRM. The RSRM paradigm provides a new framework for interpreting the well-known Kusuoka's representation of law invariant coherent risk measures and addressing inconsistency issues arising from observation/measurement errors or erroneous responses in preference elicitation process. We discuss in detail computational schemes for solving optimization problems based on the RSRM and the distributionally robust RSRM.
