Robust Joint Modeling of Outstanding Loss Reserves Data of Lines of Third Party and Auto Body Insurance of an Iranian Insurance Company: A Bayesian Approach

Outstanding loss reserves is one of the crucial actuarial issues in general insurance. In this paper, we consider a developed Bayesian method for modeling bivariate outstanding loss reserves data of lines of third party insurance and auto body insurance of an Iranian insurance company based on the bivariate Student's t and the bivariate Pearson type VII distributions. When the data does not follow the assumptions of normality, heavy-tailed distributions such as the Student's t and the Pearson type VII distributions provide robust inferences. These distributions belong to the class of the scale mixtures of normal distributions. The hierarchical structure of this class allows that under a Bayesian paradigm, the parameter estimation is simplified by sampling from normal distribution using Markov Chain Monte Carlo (MCMC) methods. We consider three models including ANOVA, ANCOVA, and random-walk for the mean of the sampling distributions. In addition, a sensitivity study to detect influential cases is performed based on the Kullback– Leibler divergence. Results show that the random-walk model under the bivariate Student's t distribution has a better performance.