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arXiv · 2509.11033

Choquet integration with submodular function on measurable space with sigma-algebra generating chain

Tetsuya Hattori
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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.

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Tetsuya Hattori. 2025-09-14. Choquet integration with submodular function on measurable space with sigma-algebra generating chain. https://arxiv.org/abs/2509.11033

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