Reserve modelling and the aggregation of risks using time varying copula models

Abstract

This paper is concerned with the appropriate claim reserving modelling and aggregation of risks in the insurance sector. In fact, literature review provided some methods to evaluate the total amount of reserves and solvency capital of different lines of business. However, these models were derived under the independent losses assumption. Thus, the total amount of reserves and capital may be inaccurate when losses are dependent, as it is the case in practice. In this paper, a novel model is proposed aiming to handle temporal dependence, both between a line of business claim's amounts and between the two lines of business claims. Generalized Autoregressive Conditional Sinistrality model is used to analyze the evolution in time of dependence and time varying copula functions are proposed to aggregate risks. To achieve such purpose, a simulation study, highlighting the impact on reserves and Solvency Capital Requirement, is performed. Results revealed that a diversification effect could be gained on the Solvency Capital when considering time varying dependence structures.