Date/Time
Date(s) - 03/12/2024
3:30 pm - 4:30 pm

Location: BSB 104

Speaker: Pengfei Cai (McMaster University)

Title: Seemingly Unrelated Regression (SUR) Copula Mixed Models for Multivariate Loss Reserving

Abstract: In property and casualty (P&C) insurance, estimating unpaid claims is crucial for an insurer’s operations.  Insurance companies often engage in multiple interrelated lines of business (LOBs), and accounting for dependence between LOBs is essential in accurately determining an insurance company’s reserve ranges and the amount of risk capital needed. Incorporating dependency into reserve calculations helps the insurer determine the appropriate amount of risk capital and leverage diversification benefit. The SUR copula regression incorporates the dependence between two LOBs through a copula using loss triangles from one company and produces a relatively large bias.  The extended Deep Triangle (EDT) models the dependence between LOBs using recurrent neural networks. The EDT model improves the reserve estimation and risk capital gain compared to the SUR copula regression model. Still, the EDT model does not provide the dependence structure between the two LOBs, and its computational cost is relatively high. Thus, we propose SUR copula mixed models to enhance SUR copula regression with multiple companies’ data for loss prediction and risk capital analysis. Due to the heterogeneous history of losses between companies and different LOBs, we model this heterogeneity using random effects and select varying distributions for losses from each LOB. This approach is illustrated with 30 pairs of loss triangles from the National Association of Insurance Commissioners database. We find that the SUR copula mixed model produces a smaller bias between predicted and actual reserves than the SUR copula regression model. We will also investigate the risk capital diversification benefits of the SUR copula mixed model.