The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model
Joint Authors
Li, Zhilong
Yi, Zhang
Limin, Wen
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-05-07
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
In the B-F reserve model, it is a very critical step to estimate the claim means of the accident year.
However, the traditional method uses the prior estimators of the claim means based on the personal experience of actuaries or historical data.
This method inevitably carries the subjectivity of the actuary himself.
In this paper, a stochastic B-F model is established, and a prior distribution is constructed for the claim means in the accident year.
The idea of the credibility theory is used to derive the linear Bayesian estimators of claim means.
Finally, the empirical Bayesian method is used to estimate the first two moments of the prior distribution, and the empirical Bayesian estimators of the claim means and the corresponding reserves are derived.
The estimators obtained in this paper do not depend on the specific forms of the sample distribution and the prior distribution and can be used directly in practice.
In the numerical simulation, our estimates are compared with the traditional B-F estimates and the chain ladder estimates.
It is verified that the estimates given in this paper have small mean square error.
American Psychological Association (APA)
Yi, Zhang& Limin, Wen& Li, Zhilong. 2020. The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1196483
Modern Language Association (MLA)
Yi, Zhang…[et al.]. The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model. Mathematical Problems in Engineering No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1196483
American Medical Association (AMA)
Yi, Zhang& Limin, Wen& Li, Zhilong. The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1196483
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1196483