Multidimensional credibility: A new approach based on joint distribution function

Wen, Limin1; Liu, Wei1; Zhang, Yiying2

2024-04-01

10.1017/asb.2024.13

ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION   影响因子和分区

0515-0361

1783-1350

In the traditional multidimensional credibility models developed by Jewell ((1973) Operations Research Center, pp. 73-77.), the estimation of the hypothetical mean vector involves complex matrix manipulations, which can be challenging to implement in practice. Additionally, the estimation of hyperparameters becomes even more difficult in high-dimensional risk variable scenarios. To address these issues, this paper proposes a new multidimensional credibility model based on the conditional joint distribution function for predicting future premiums. First, we develop an estimator of the joint distribution function of a vector of claims using linear combinations of indicator functions based on past observations. By minimizing the integral of the expected quadratic distance function between the proposed estimator and the true joint distribution function, we obtain the optimal linear Bayesian estimator of the joint distribution function. Using the plug-in method, we obtain an explicit formula for the multidimensional credibility estimator of the hypothetical mean vector. In contrast to the traditional multidimensional credibility approach, our newly proposed estimator does not involve a matrix as the credibility factor, but rather a scalar. This scalar is composed of both population information and sample information, and it still maintains the essential property of increasingness with respect to the sample size. Furthermore, the new estimator based on the joint distribution function can be naturally extended and applied to estimate the process covariance matrix and risk premiums under various premium principles. We further illustrate the performance of the new estimator by comparing it with the traditional multidimensional credibility model using bivariate exponential-gamma and multivariate normal distributions. Finally, we present two real examples to demonstrate the findings of our study.

Multidimensional credibility joint distribution premium principles Frobenius norm consistency asymptotic normality G21 G22 G31

SCI ; SSCI

英语

通讯

Jiangxi Provincial Natural Science foundation[20224BCD41001] ; Jiangxi Provincial Graduate Innovation Fund[YC2022-s285] ; National Natural Science Foundation of China["12101336","72311530687"] ; GuangDong Basic and Applied Basic Research Foundation[2023A1515011806] ; Shenzhen Science and Technology Program[JCYJ20230807093312026]

Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences

Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods ; Statistics & Probability

WOS:001201293000001

CAMBRIDGE UNIV PRESS

Web of Science

1.Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

Wen, Limin,Liu, Wei,Zhang, Yiying. Multidimensional credibility: A new approach based on joint distribution function[J]. ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION,2024.

Wen, Limin,Liu, Wei,&Zhang, Yiying.(2024).Multidimensional credibility: A new approach based on joint distribution function.ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION.

Wen, Limin,et al."Multidimensional credibility: A new approach based on joint distribution function".ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION (2024).