Representation of increasing convex functionals with countably additive measures

Patrick Cheridito; Michael Kupper; Ludovic Tangpi

doi:10.4064/sm181107-16-2

Representation of increasing convex functionals with countably additive measures

Patrick Cheridito, Michael Kupper, Ludovic Tangpi

Operations Research & Financial Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a suprepresentation of functionals defined on spaces of real-valued Borel measurable functions. Our assumptions consist of sequential semicontinuity conditions which are easy to verify in different applications.

Original language	English (US)
Pages (from-to)	121-140
Number of pages	20
Journal	Studia Mathematica
Volume	260
Issue number	2
DOIs	https://doi.org/10.4064/sm181107-16-2
State	Published - 2021

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Countably additive measures
Increasing convex functionals
Regular measures
Representation theorems

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10.4064/sm181107-16-2

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AB - We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a suprepresentation of functionals defined on spaces of real-valued Borel measurable functions. Our assumptions consist of sequential semicontinuity conditions which are easy to verify in different applications.

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KW - Increasing convex functionals

KW - Regular measures

KW - Representation theorems

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Representation of increasing convex functionals with countably additive measures

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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