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Agbeko, Tony, Munir Hiabu, Mara Dolores Martnez-Miranda, Jens Perch Nielsen, and Richard Verrall. 2014. “Validating the Double Chain Ladder Stochastic Claims Reserving Model.” Variance 8 (2): 138–60.
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  • Figure 1. Motor BI, chain ladder estimated parameters, underwriting \(\hat{\alpha}_i\) and development \(\hat{\beta}_j\), and DCL estimates of severity inflation \(\hat{\gamma}_i\) and delay \(\hat{\pi}_k\) (“general” refers to the solutions of the linear system described in Section 3.1 and “adjusted” refers to the adjusted values which are defined afterwards and denoted by \(\hat{\tilde{\pi}}_k\)).
  • Figure 2. Motor PD, chain ladder estimated parameters, underwriting \(\hat{\alpha}_i\) and development \(\hat{\beta}_j\), and DCL estimates of severity inflation \(\hat{\gamma}_i\) and delay \(\hat{\pi}_k\).
  • Figure 3. Motor BI, BDCL estimated parameters, underwriting \(\alpha_i\) and development \(\beta_j\), and DCL estimates of severity inflation \(\gamma_i\) and delay \(\pi_k\).
  • Figure 4. Motor PD, BDCL estimated parameters, underwriting \(\alpha_i\) and development \(\beta_j\), and DCL estimates of severity inflation \(\gamma_i\) and delay \(\pi_k\).
  • Figure 5. Motor BI, IDCL estimated parameters, underwriting \(\alpha_i\) and development \(\beta_j\), and DCL estimates of severity inflation \(\gamma_i\) and delay \(\pi_k\).
  • Figure 6. Motor PD, IDCL estimated parameters, underwriting \(\alpha_i\) and development \(\beta_j\), and DCL estimates of severity inflation \(\gamma_i\) and delay \(\pi_k\).
  • Figure 7. Motor BI, estimated inflation parameters for DCL, BDCL, and IDCL.
  • Figure 8. Motor PD, estimated inflation, parameters for DCL, BDCL, and IDCL.
  • Figure 9. Index sets for aggregate claims data, assuming a maximum delay \(m - 1\).
  • Figure 10. Motor BI settlement pattern.
  • Figure 11. Motor PD settlement pattern.
  • Figure 12. Calendar years used for development factors.
  • Figure 13. Back testing and prediction errors.
  • Figure 14. Box plot of the DCL, BDCL and IDCL cell error quartiles.

Abstract

Double chain ladder, introduced by Martínez-Miranda et al. (2012), is a statistical model to predict outstanding claim reserve. Double chain ladder and Bornhuetter-Ferguson are extensions of the originally described double chain ladder model which gain more stability through including expert knowledge via an incurred claim amounts triangle. In this paper, we introduce a third method, the incurred double chain ladder, which replicates the popular results from the classical chain ladder on incurred data. We will compare and validate these three using two datasets from major property and casualty insurers.