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Risk comparisons of premium rules: optimality and a life insurance study

Asmussen, Sören LU and Moller, JR (2003) In Insurance, Mathematics & 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)
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author
organization
publishing date
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 & 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
2007-08-22 13:25:37
date last changed
2018-05-29 10:30:38
@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},
  keyword      = {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 & 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},
  volume       = {32},
  year         = {2003},
}