In this paper, we consider the quantitative stability of a class of risk-averse multistage stochastic programs, whose objective functions are defined by multi-period $ p $th order lower partial moments (LPM) with given targets, and their distributionally robust counterparts. We first derive the upper bounds of feasible solutions as preliminaries. Then, by employing calm modifications, the quantitative stability results are obtained under a special measurable perturbation of stochastic process, which extend the present results under risk-neutral cases to risk-averse ones. Moreover, we recast the risk-averse model by probability measures of stochastic process, and obtain new quantitative stability estimations on the basis of proper probability metrics under the general perturbation of stochastic process. Finally, motivated by the availability of only partial information about probability measures, we further consider the distributionally robust counterpart of our recasting model, and establish the discrepancy of optimal values with respect to the perturbation of ambiguity sets.

中文翻译：

---

一类风险规避多阶段随机程序的稳定性及其分布稳健的对应项

在本文中，我们考虑了一类风险规避多阶段随机程序的定量稳定性，其目标函数由具有给定目标的多周期 $p$th 阶低偏矩 (LPM) 及其分布稳健的对应项定义。我们首先推导出可行解的上限作为初步。然后，通过使用平静修正，在随机过程的特殊可测量扰动下获得定量稳定性结果，将风险中性情况下的现有结果扩展到风险规避情况。此外，我们通过随机过程的概率度量重铸风险规避模型，并在随机过程的一般扰动下根据适当的概率度量获得新的定量稳定性估计。最后，