Loading monotonicity of weighted premiums, and total positivity properties of weight functions
© 2019 Elsevier Inc. 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 part...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/135114 |
| _version_ | 1826215998202576896 |
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| author | Richards, Donald Uhler, Caroline |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Richards, Donald Uhler, Caroline |
| author_sort | Richards, Donald |
| collection | MIT |
| description | © 2019 Elsevier Inc. 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. |
| first_indexed | 2024-09-23T16:40:45Z |
| format | Article |
| id | mit-1721.1/135114 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:40:45Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1351142023-03-24T19:28:31Z Loading monotonicity of weighted premiums, and total positivity properties of weight functions Richards, Donald Uhler, Caroline Massachusetts Institute of Technology. Laboratory for Information and Decision Systems © 2019 Elsevier Inc. 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. 2021-10-27T20:10:48Z 2021-10-27T20:10:48Z 2019 2019-07-09T18:07:08Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135114 en 10.1016/j.jmaa.2019.02.054 Journal of Mathematical Analysis and Applications Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Richards, Donald Uhler, Caroline Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title | Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title_full | Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title_fullStr | Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title_full_unstemmed | Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title_short | Loading monotonicity of weighted premiums, and total positivity properties of weight functions |
| title_sort | loading monotonicity of weighted premiums and total positivity properties of weight functions |
| url | https://hdl.handle.net/1721.1/135114 |
| work_keys_str_mv | AT richardsdonald loadingmonotonicityofweightedpremiumsandtotalpositivitypropertiesofweightfunctions AT uhlercaroline loadingmonotonicityofweightedpremiumsandtotalpositivitypropertiesofweightfunctions |