An Accurate Asymptotic Approximation for Experience Rated Premiums

Gatto, Riccardo (2004). An Accurate Asymptotic Approximation for Experience Rated Premiums. ASTIN bulletin, 34(1), pp. 113-124. Cambridge University Press 10.1017/S051503610001391X

[img]
Preview
Text
S051503610001391X.pdf - Published Version
Available under License Publisher holds Copyright.

Download (163kB) | Preview

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Gatto, Riccardo

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0515-0361

Publisher:

Cambridge University Press

Language:

English

Submitter:

Marceline Brodmann

Date Deposited:

21 Jul 2020 08:24

Last Modified:

25 Jul 2020 12:12

Publisher DOI:

10.1017/S051503610001391X

BORIS DOI:

10.7892/boris.115909

URI:

https://boris.unibe.ch/id/eprint/115909

Actions (login required)

Edit item Edit item
Provide Feedback