Choquet integration with submodular function on measurable space with sigma-algebra generating chain
Probability
2025-09-16 v1
Abstract
Based on a study of a formula representing submodular set function as a supremum of measures dominated by the set function, we present a corresponding formula for a Choquet integration with respect to the set function, on a measurable space which has a chain of measurable set generating the sigma-algebra. As an application we reproduce a basic formula in mathematical finance on law invariant coherent risk measures. We also study a recursion relation of set functions for which the representation formula characterizes the fixed point.
Cite
@article{arxiv.2509.11033,
title = {Choquet integration with submodular function on measurable space with sigma-algebra generating chain},
author = {Tetsuya Hattori},
journal= {arXiv preprint arXiv:2509.11033},
year = {2025}
}