Chapter 6 LDF Curve-Fitting and Stochastic Reserving: A Maximum Likelihood Approach - D. Clark

\(\star\) Paper definition/standards:

• We use the average age of the period here (so minus 6 month)

• Ratio of variance to mean is constant, \(\sigma^2\), for the whole triangle (6.3)

  • Variance of incremental loss is proportional to the mean of incremental loss and assume this proportion is known and same for the whole triangle

Reserve estimate

• \(\star \star\) Given \(G(x)\) distribution

  • Loglogistic (6.1), or

  • Weibull (6.2)

  • Might have to estimate parameters

• 2 Reserving method

  • \(\star\) LDF Method

  • \(\star\) Cape Cod Method

    • Typically better because it has additional information on exposure

• Test for truncation by looking at age twice the triangle size

  • Different truncation method

Reserve process variance

• \(\star \star\) Need Estimation of \(\sigma^2\) (6.4)

  • Note the \(n\) and \(p\) for the 2 methods

  • We’re looking at incremental losses

Distribution

• Process variance

• ODP for incremental loss (6.5)

• Parameter variance

• Estimate using MLE 6.1

  • Estimate for \(ULT_{AY}\) based on MLE

  • Estimate for \(ELR\) based on MLE

3 key assumptions

• \(\star \star\) Test \(iid\) assumpation with residual plots

Other use of the model

• Estimate variance for next prospective u/w year

• Estimate CY development

• Variability in discounted reserve

Counting average accident date