Weak Continuity of Risk Functionals with Applications to Stochastic Programming
Weak Continuity of Risk Functionals with Applications to Stochastic Programming
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DOI：
10.1137/15m1048689
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
M. Claus;Volker Krätschmer;R. Schultz
中科院分区：
文献类型：
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作者：
M. Claus;Volker Krätschmer;R. Schultz
在随机不确定环境下，风险的度量和管理已成为现代决策的关键。在两阶段随机规划中，平均风险模型本质上是由一个参数追索问题和一个风险量化定义的。从定性稳健性理论的角度，我们讨论了所得到的目标函数关于潜在概率测度的扰动连续的充分条件。我们的方法涵盖了相当广泛的一类与随机规划相关的风险度量和相关的追索权模型。这不仅统一了以往的方法，而且将已知的两阶段随机规划的稳定性结果分别推广到具有混合整数二次资源和混合整数凸资源的模型。
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From the perspective of qualitative robustness theory, we discuss sufficient conditions for continuity of the resulting objective functions with respect to perturbation of the underlying probability measure. Our approach covers a fairly comprehensive class of both stochastic programming related risk measures and relevant recourse models. Not only does this unify previous approaches but also extends known stability results for two-stage stochastic programs to models with mixed-integer quadratic recourse and mixed-integer convex recourse, respectively.