Dependence modelling on loss triangles

The methods of calculation for claims reserving assume that claims are independent. However, dependencies that occur between lines of business, such as accident year dependence, development year dependence, and calendar year dependence create a dependency between claim amounts. In this study, we assume an unobserved random effect between and within lines of business. In order to model this effect, we propose a copula regression model with unobserved random effect in which we consider additive and multiplicative effect structure. We consider four different random effect distributions in order to model unobserved random effect. The theoretical results are illustrated on a real loss triangle data set for two dependent lines of business. Regarding to the results, we determine that suggested model performs better than classical models.