Risk comparisons of premium rules: optimality and a life insurance study
(2003) In Insurance: Mathematics and Economics 32(3). p.331-344- Abstract
- Consider a risk Y-1 (x) depending on an observable covariate x which is the outcome of a random variable A with a known distribution, and consider a premium p(x) of the form p(x) = EY1 (x) + etap(1) (x). The corresponding adjustment coefficient gamma is the solution of E exp{gamma[Y-1(A) - p(A)]} = 1, and we characterize the rule for the loading premium p(1)((.)) which maximizes gamma subject to the constraint Ep(1) (A) = 1. In a life insurance study, the optimal p(1)(*)((.)) is compared to other premium principles like the expected value, the variance and the standard deviation principles as well as the practically important rules based on safe mortality rates (i.e., using the first order basis rather than the third order one). The life... (More)
- Consider a risk Y-1 (x) depending on an observable covariate x which is the outcome of a random variable A with a known distribution, and consider a premium p(x) of the form p(x) = EY1 (x) + etap(1) (x). The corresponding adjustment coefficient gamma is the solution of E exp{gamma[Y-1(A) - p(A)]} = 1, and we characterize the rule for the loading premium p(1)((.)) which maximizes gamma subject to the constraint Ep(1) (A) = 1. In a life insurance study, the optimal p(1)(*)((.)) is compared to other premium principles like the expected value, the variance and the standard deviation principles as well as the practically important rules based on safe mortality rates (i.e., using the first order basis rather than the third order one). The life insurance model incorporates premium reserves, discounting, and interest return on the premium reserve but not on the free reserve. Bonus is not included either. (C) 2003 Published by Elsevier Science B.V. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/297978
- author
- Asmussen, Sören LU and Moller, JR
- organization
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- whole life insurance, third order basis, premium, loading, life annuities, large deviations, Gompertz-Makeham law, basis, first order, delayed claims, adjustment coefficient, convex ordering, shot noise
- in
- Insurance: Mathematics and Economics
- volume
- 32
- issue
- 3
- pages
- 331 - 344
- publisher
- Elsevier
- external identifiers
-
- wos:000184767500001
- scopus:0041841497
- ISSN
- 1873-5959
- DOI
- 10.1016/S0167-6687(02)00208-1
- language
- English
- LU publication?
- yes
- id
- e16ed1cd-1387-4229-a43e-3f02296145aa (old id 297978)
- date added to LUP
- 2016-04-01 12:04:52
- date last changed
- 2022-04-21 02:09:19
@article{e16ed1cd-1387-4229-a43e-3f02296145aa,
abstract = {{Consider a risk Y-1 (x) depending on an observable covariate x which is the outcome of a random variable A with a known distribution, and consider a premium p(x) of the form p(x) = EY1 (x) + etap(1) (x). The corresponding adjustment coefficient gamma is the solution of E exp{gamma[Y-1(A) - p(A)]} = 1, and we characterize the rule for the loading premium p(1)((.)) which maximizes gamma subject to the constraint Ep(1) (A) = 1. In a life insurance study, the optimal p(1)(*)((.)) is compared to other premium principles like the expected value, the variance and the standard deviation principles as well as the practically important rules based on safe mortality rates (i.e., using the first order basis rather than the third order one). The life insurance model incorporates premium reserves, discounting, and interest return on the premium reserve but not on the free reserve. Bonus is not included either. (C) 2003 Published by Elsevier Science B.V.}},
author = {{Asmussen, Sören and Moller, JR}},
issn = {{1873-5959}},
keywords = {{whole life insurance; third order basis; premium; loading; life annuities; large deviations; Gompertz-Makeham law; basis; first order; delayed claims; adjustment coefficient; convex ordering; shot noise}},
language = {{eng}},
number = {{3}},
pages = {{331--344}},
publisher = {{Elsevier}},
series = {{Insurance: Mathematics and Economics}},
title = {{Risk comparisons of premium rules: optimality and a life insurance study}},
url = {{http://dx.doi.org/10.1016/S0167-6687(02)00208-1}},
doi = {{10.1016/S0167-6687(02)00208-1}},
volume = {{32}},
year = {{2003}},
}