On the Lebesgue Property of Monotone Convex Functions
Functional Analysis
2014-03-14 v2 Optimization and Control
Probability
Risk Management
Abstract
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous linear functionals. This generalizes and unifies several recent results obtained in the context of convex risk measures.
Keywords
Cite
@article{arxiv.1305.2271,
title = {On the Lebesgue Property of Monotone Convex Functions},
author = {Keita Owari},
journal= {arXiv preprint arXiv:1305.2271},
year = {2014}
}
Comments
8 pages, to appear in Mathematics and Financial Economics