|
Exploring limits for the Pearson Correlation Coefficient and its Application for Study of Insurance Losses
|
Rahim Mahmoudvand *   |
| Bu-Ali Sina University |
|
|
Abstract: (148 Views) |
Actuarial studies treat insurance losses as random variables, and appropriate probabilistic models are sought to model them. Since losses are evaluated in terms of a unitary amount, distributions with positive support are typically used to model them. However, in practice, losses are often bounded due to policyholder conditions, which must be considered when modeling. While this is not a problem for univariate cases, it becomes complicated for multivariate cases. Copulas can be helpful in such situations, but studying the correlation is crucial in the first step. Therefore, this paper addresses the problem of investigating the effect of restricted losses on correlation in multivariate cases.
The Pearson correlation coefficient is a widely used measure of linear correlation between variables. In this study, we examine the correlation between two random variables and investigate the estimator of the correlation coefficient. Furthermore, we analyze a real-world dataset from an Iranian insurance company, including losses due to physical damage and bodily injury as covered by third-party liability insurance.
Upper and lower limits for both the Pearson correlation coefficient and its estimator were derived. The Copula method was employed to obtain the bounds for the correlation parameters, while order statistics were used to obtain the bounds for the sample correlation coefficient. Furthermore, two methods were used to determine the correlation between physical damage and bodily injury, and the results were compared.
Our findings suggest that the commonly used upper and lower bounds of -1 and +1 for the Pearson correlation coefficient may not always apply to insurance losses. Instead, our analysis reveals that narrower bounds can be established for this measure in such cases. The results of this study provide important insights into modeling insurance losses in multivariate cases and have practical implications for risk management and pricing decisions in the insurance industry.
|
|
| Keywords: Order Statistics, Moment, Confinement. |
|
|
Full-Text [PDF 256 kb]
(96 Downloads)
|
Type of Study: Research |
Subject:
Special
Received: 2023/09/24 | Accepted: 2024/03/13 | Published: 2024/03/15
|
|
|
|
|
|
|
| Send email to the article author |
|
|
|
| Add your comments about this article |
|
|
|
