Quantifying non-monotonicity of functions and the lack of positivity in signed measures
Volume 4, Issue 3 (2017), pp. 219–231
Pub. online: 28 September 2017
Type: Research Article
Open Access
Open Access
Received
16 June 2017
16 June 2017
Revised
5 September 2017
5 September 2017
Accepted
5 September 2017
5 September 2017
Published
28 September 2017
28 September 2017
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.
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