Document Type : Original Research Paper

Authors

• M. Goudarzi ¹
• M. Zokaei ²

¹ Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

² Department of Bimometry, School of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

Abstract

Saving deferred losses is one of the most fundamental issues in general insurance. In this article, a generalized Bayesian method is used to model the storage of deferred loss data in the fields of body insurance and third party automobile insurance of an Iranian insurance company using Student's t and Pearson's 7th type bivariate distributions. When the data do not follow the assumption of normality, heavy-tailed distributions such as Student's t and Pearson type 7 lead to more robust inferences. These distributions belong to the category of mixed-scale normal distributions. The hierarchical structure of this category allows parameter estimation to be done easily using Markovian chain Monte Carlo methods in the Bayesian framework. For mean sampling distributions, three models of analysis of variance, analysis of covariance, and random walk are considered. In addition, to identify effective samples, a sensitivity analysis study has been conducted based on the Kolbeck-Leibler divergence in the models. The results show that the random walk model with the bivariate Student's t distribution has a better performance for damage payments.

Keywords

• Outstanding loss reserves
• Scale mixtures of normal distributions
• Bayesian inference
• Case deletion
• Kullback– Leibler divergence