27.11 Stochastic Loss Reserving Using Bayesian MCMC Models - G. Meyer

Interpretation of all the test:

• KS-test: (11.1), (11.2), and (11.3)

• \(p-p\) plot (fig. 11.1)

  • Too light tailed: Shallow slope near corner and steep in the middle

  • Too heavy tailed: Steep slope near corner and shallow in the middle

  • Biased upwards: Bow down

• Freq vs Count plot (fig. 11.2)

Bayesian Models (Cumulative):

• Lognormal (11.4)

• \(\beta = 0\) when it’s done developing

• \(\sigma\) constraint (11.6)

Variations

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

  • Mean (11.5)

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

  • Mean (11.7)

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

  • Mean (11.8)

  • $>0 $ for increase payout speed

Bayesian Models (Incremental):

• Distribution (11.11)

  • Based on mixed lognormal distribution (11.10) (skewed log-normal (11.9) was not used)

• \(\sigma\) constraint (11.13) is different

• Additional constraint on \(\beta\) so that it is decreasing

• Constraint on CY trend \(\tau\)

• Additional constraint on \(\sigma\) so that it cannot increase drastically period to period

Variation

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

  • Mean (11.12)

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