Credibility Theory for Variance Premium Principle

Yong, Yaodi; Zeng, Pingping; Zhang, Yiying

2024-06-01

10.1080/10920277.2023.2299497

NORTH AMERICAN ACTUARIAL JOURNAL   影响因子和分区

1092-0277

2325-0453

The method of credibility theory plays a critical role in various research areas of actuarial science. Among others, the hypothetical mean and process variance are two quantities that convey crucial information to insurance companies when determining premiums for the insureds. The classical credibility model charges premiums by applying a linear combination of the mean of past claims and the population mean, and the corresponding estimator is proved to be the best estimator of the hypothetical mean under the mean squared loss criterion. Enlightened by the prestigious variance premium principle, we propose a credibility approach to estimate the linear combination of hypothetical mean and process variance under the quadratic loss function. Our proposed estimator consists of the linear form of observations and their quadratic terms, as well as some quantities representing population information. Meanwhile, a spin-off result is found and utilized to compare with the classical credibility model and the q-credibility model. The nonparametric estimators of structural quantities are also provided for ease of practical usage. Several numerical illustrations are carried out to demonstrate the performance of the estimator. A real dataset from a Swiss insurance company is also analyzed for the practical application of our results, where a data-driven procedure is proposed for determining the safety loading.

ESCI

英语

第一 ; 通讯

National Natural Science Foundation of China["12171228","11701266","12101336","72311530687"] ; Guangdong Basic and Applied Basic Research Foundation[2023A1515011806] ; Shenzhen Science and Technology Program[JCYJ20230807093312026]

Business & Economics

Business, Finance

WOS:001259312300001

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD

Web of Science

Southern Univ Sci & Technol, Dept Math, 1088 Xueyuan Rd, Shenzhen 518055, Guangdong, Peoples R China

Yong, Yaodi,Zeng, Pingping,Zhang, Yiying. Credibility Theory for Variance Premium Principle[J]. NORTH AMERICAN ACTUARIAL JOURNAL,2024.

Yong, Yaodi,Zeng, Pingping,&Zhang, Yiying.(2024).Credibility Theory for Variance Premium Principle.NORTH AMERICAN ACTUARIAL JOURNAL.

Yong, Yaodi,et al."Credibility Theory for Variance Premium Principle".NORTH AMERICAN ACTUARIAL JOURNAL (2024).