Loading monotonicity of weighted premiums, and total positivity properties of weight functions

Donald Richards, Caroline Uhler

Research output: Contribution to journalArticle

Abstract

We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of generalized weighted premiums; in particular, we deduce for weight functions that are totally positive of order three a monotonicity property of the variance-to-mean ratio, or index of dispersion, of the loss variable. We derive the higher order total positivity properties of some ratios that arise in actuarial and insurance analysis of combined risks. Further, we examine seven classes of weight functions that have appeared in the literature and we ascertain the higher order total positivity properties of those functions.

Original languageEnglish (US)
Pages (from-to)532-553
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume475
Issue number1
DOIs
StatePublished - Jul 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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