On Extendability of the Principle of Equivalent Utility
An insurance premium principle is a way of assigning to every risk a real number, interpreted as a premium for insuring risk. There are several methods of defining the principle. In this paper, we deal with the principle of equivalent utility under the rank-dependent utility model. The principle, ge...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-12-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/1/42 |
| _version_ | 1811298439413104640 |
|---|---|
| author | Małgorzata Chudziak Marek Żołdak |
| author_facet | Małgorzata Chudziak Marek Żołdak |
| author_sort | Małgorzata Chudziak |
| collection | DOAJ |
| description | An insurance premium principle is a way of assigning to every risk a real number, interpreted as a premium for insuring risk. There are several methods of defining the principle. In this paper, we deal with the principle of equivalent utility under the rank-dependent utility model. The principle, generated by utility function and probability distortion function, is based on the assumption of the symmetry between the decisions of accepting and rejecting risk. It is known that the principle of equivalent utility can be uniquely extended from the family of ternary risks. However, the extension from the family of binary risks need not be unique. Therefore, the following problem arises: characterizing those principles that coincide on the family of all binary risks. We reduce the problem thus to the multiplicative Pexider functional equation on a region. Applying the form of continuous solutions of the equation, we solve the problem completely. |
| first_indexed | 2024-04-13T06:19:19Z |
| format | Article |
| id | doaj.art-ba025e53270f4ea1b8ff0a7751a28c3c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:19:19Z |
| publishDate | 2019-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ba025e53270f4ea1b8ff0a7751a28c3c2022-12-22T02:58:42ZengMDPI AGSymmetry2073-89942019-12-011214210.3390/sym12010042sym12010042On Extendability of the Principle of Equivalent UtilityMałgorzata Chudziak0Marek Żołdak1Institute of Mathematics, University of Rzeszów, Pigonia 1, 35-959 Rzeszów, PolandInstitute of Mathematics, University of Rzeszów, Pigonia 1, 35-959 Rzeszów, PolandAn insurance premium principle is a way of assigning to every risk a real number, interpreted as a premium for insuring risk. There are several methods of defining the principle. In this paper, we deal with the principle of equivalent utility under the rank-dependent utility model. The principle, generated by utility function and probability distortion function, is based on the assumption of the symmetry between the decisions of accepting and rejecting risk. It is known that the principle of equivalent utility can be uniquely extended from the family of ternary risks. However, the extension from the family of binary risks need not be unique. Therefore, the following problem arises: characterizing those principles that coincide on the family of all binary risks. We reduce the problem thus to the multiplicative Pexider functional equation on a region. Applying the form of continuous solutions of the equation, we solve the problem completely.https://www.mdpi.com/2073-8994/12/1/42insurance premiumextensionutility functionprobability distortion functionchoquet integralpexider functional equation |
| spellingShingle | Małgorzata Chudziak Marek Żołdak On Extendability of the Principle of Equivalent Utility Symmetry insurance premium extension utility function probability distortion function choquet integral pexider functional equation |
| title | On Extendability of the Principle of Equivalent Utility |
| title_full | On Extendability of the Principle of Equivalent Utility |
| title_fullStr | On Extendability of the Principle of Equivalent Utility |
| title_full_unstemmed | On Extendability of the Principle of Equivalent Utility |
| title_short | On Extendability of the Principle of Equivalent Utility |
| title_sort | on extendability of the principle of equivalent utility |
| topic | insurance premium extension utility function probability distortion function choquet integral pexider functional equation |
| url | https://www.mdpi.com/2073-8994/12/1/42 |
| work_keys_str_mv | AT małgorzatachudziak onextendabilityoftheprincipleofequivalentutility AT marekzołdak onextendabilityoftheprincipleofequivalentutility |