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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Richards, Donald¹  Uhler, Caroline^2,3 

[1] Penn State Univ, Dept Stat, University Pk, PA 16802 USA

[2] MIT, Lab Informat & Decis Syst, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[3] MIT, Inst Data Syst & Soc, 77 Massachusetts Ave, Cambridge, MA 02139 USA

关键词: Binet-Cauchy formula;    Index of dispersion;    Loading parameter;    Total positivity;    Variance-to-mean ratio;    Weighted premiums;   

DOI  :  10.1016/j.jmaa.2019.02.054

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free