Quantifying non-monotonicity of functions and the lack of positivity in signed measures

TL;DR

This paper introduces a method to quantify the non-monotonicity and lack of positivity in functions and signed measures, with applications in decision making fields like finance and economics.

Contribution

It develops a novel approach for measuring non-monotonicity and sign-constancy in functions and signed measures, addressing a gap in existing quantitative tools.

Findings

Method effectively quantifies non-monotonicity.

Applicable to signed measures in finance and economics.

Enhances decision-making analysis with new metrics.

Abstract

In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In this paper we develop a method designed specifically for this task, including quantification of the lack of positivity, negativity, or sign-constancy in signed measures. We note relevant applications in Insurance, Finance, and Economics, and discuss some of them in detail.