Chapter 10 Obtaining Predictive Distributions for Reserves Which Incorporate Expert Opinions - R. Verrall

Model is defined with (ODP or ODNB) and stochastic row parameters

• Moments for Mack: (10.1) & (10.2)

• Moments for ODP: (10.3)

• Moments fod OD NB: (10.6)

Chainladder intervention

• Variance of prior and it’s impact

\(\star\) Bayesian BF calculation:

• Gamma moments (10.10)

  • Impact of \(\beta_i\) on the Gamma variance

• \(\star\) Credibility formula (10.11) and credibility weight (10.12)

  • \(\beta_i\) and \(\varphi\) impact the credibility weight

Use and calculate the stochastic column parameters

• \(\star\) Use the parameters with (10.13), see fig. 10.1

• \(\star\) Calculate the parameters \(\gamma_i\) pictorially, see fig. 10.2