SIAM Journal on Optimization, Volume 30, Issue 1, Page 377-406, January 2020.
We consider a two-stage stochastic bilevel linear program where the leader contemplates the follower's reaction at the second stage optimistically. In this setting, the leader's objective function value can be modeled by a random variable, which we evaluate based on some law-invariant (quasi-)convex risk measure. After establishing Lipschitzian properties and existence results, we derive sufficient conditions for differentiability when the choice function is a Lipschitzian transformation of the expectation. This allows us to formulate first-order necessary optimality conditions for models involving certainty equivalents or expected disutilities. Moreover, a qualitative stability result under perturbation of the underlying probability distribution is presented. Finally, for finite discrete distributions, we reformulate the bilevel stochastic problems as standard bilevel problems and propose a regularization scheme for solving a deterministic bilevel programming problem.

中文翻译：

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二层随机线性规划中的规避风险模型

SIAM优化杂志，第30卷，第1期，第377-406页，2020年1月。
我们考虑一个两阶段的随机双线性计划，其中领导者乐观地考虑了跟随者在第二阶段的反应。在这种情况下，领导者的目标函数值可以由随机变量建模，我们可以根据一些法律不变的（准）凸风险度量对其进行评估。建立Lipschitz的性质和存在的结果后，我们得到的充分条件可微的时候选择功能是期望的Lipschitz的转变。这使我们能够为涉及确定性等价物或预期效用的模型制定一阶必要最优条件。此外，提出了在潜在概率分布扰动下的定性稳定性结果。最后，对于有限离散分布，