11.4 Models Overview

Starting point for the Bayesian models were to relax some of the assumptions of the Mack method:

• LCL: Relaxes the first assumption where Mack treats loss to date as a fixed level parameters

• CCL: Builds on top of LCL and allows for AY correlations, which relaxes the 2^nd assumption of Mack

Prior distributions

• Paper uses diffuse prior for the most part since the author doesn’t have direct knowledge of the business

• Given more direct knowledge of the underlying business, we can specify more restrictive priors for \(\{\alpha_w\}\) and \(logelr\)

Bayesian Models:

• Leveled Chain-Ladder (LCL): Add variability to the row parameter

• Correlated Chain-Ladder (CCL): Add AY correlation \(\rho\)

• Leveled Incremental Trend (LIT): Use skewed distribution and CY trend \(\tau\)

• Correlated Incremental Trend (CIT): LIT with added AY correlation \(\rho\)

• Changing Settlement Rate (CSR): LCL with speed up claims closure \(\gamma\)

Figure 11.3: Overview of models

Non-Bayesian Models:

• Mack: See Mack-1994

• England & Verall ODP: See Shapland, but doesn’t have the residual adjustments

Remark. Non-Bayesian Models

• Mack is the only one that does not have a base form of \(\mu_{wd} = \alpha_w + \beta_d\)

• ODP is the England & Verall Bootstrap