Risk forms: representation, disintegration, and application to partially observable two-stage systems
Risk forms: representation, disintegration, and application to partially observable two-stage systems
复制标题
风险形式：表示、分解以及在部分可观测两阶段系统中的应用
DOI：
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发表时间：
2019
影响因子：
2.7
通讯作者：
A. Ruszczynski
中科院分区：
文献类型：
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作者：
Darinka Dentcheva;A. Ruszczynski
我们引入了风险形式的概念，它是两个参数的实函数：波兰空间上的可测函数和该空间上的测度。我们将对偶理论和 Kusuoka 表示推广到这种情况。对于作用于波兰空间乘积的风险形式，我们定义了边际形式和条件形式，并证明了一个分解公式，该公式将风险形式表示为其边际形式和条件形式的组合。我们将所提出的方法应用于具有部分信息和决策相关观测分布的两阶段随机规划问题。
We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We generalize the duality theory and the Kusuoka representation to this setting. For a risk form acting on a product of Polish spaces, we define marginal and conditional forms and we prove a disintegration formula, which represents a risk form as a composition of its marginal and conditional forms. We apply the proposed approach to two-stage stochastic programming problems with partial information and decision-dependent observation distribution.