Risk Forms: Representation, Disintegration, and Application to Partially Observable Two-Stage Systems
Optimization and Control
2018-11-20 v2
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.
Cite
@article{arxiv.1807.02300,
title = {Risk Forms: Representation, Disintegration, and Application to Partially Observable Two-Stage Systems},
author = {Darinka Dentcheva and Andrzej Ruszczynski},
journal= {arXiv preprint arXiv:1807.02300},
year = {2018}
}