6.6 Other Use of Model
6.6.1 Variance of Prospective Losses
Estimate variance for the next u/w year
- Need to be given the \(\mathrm{Var}(ELR)\)
Process Variance:
\[\sigma^2 \times \: ELR \: \times Premium\]
Parameter Variance:
\[\left(\sqrt{\mathrm{Var}(ELR)}\times Premium \right)^2\]
Total Variance: Process Variance + Parameter Variance
CoV:
\[\dfrac{\sqrt{Total \: Variance}}{ELR \times Premium}\]
6.6.2 Calendar Year Development
Estimated paid losses over the next 12 months:
\[[G(x+12) - G(x)] \times a \: priori \:Ultimate\]
No truncation here
a priori from the LDF method here
Sum for all AYs and compare with actual calendar year emergence
Can calculate the s.d. to see if it’s in range (process var is still \(\sigma^2 \times\) estimate)
6.6.3 Variability in the Discounted Reserves
Similar to the above, but CoV will be smaller since the tail with the most variability gets discounted the most