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arXiv · 1807.02300

Risk Forms: Representation, Disintegration, and Application to Partially Observable Two-Stage Systems

Darinka Dentcheva·Andrzej Ruszczynski
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Abstract

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.

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Darinka Dentcheva, Andrzej Ruszczynski. 2018-07-06. Risk Forms: Representation, Disintegration, and Application to Partially Observable Two-Stage Systems. https://arxiv.org/abs/1807.02300

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