7.8 Aggregate Limits

Use collective risk model to model individual losses

• Poisson (frequency) and Weibull (severity)

• Build out a table with XS loss for each deductible and aggregate

• Need a different model for each age?

Need 4 inputs:

1. Expected unlimited

2. Age

3. Deductible

4. Aggregate limit

Reserve (use BF): Expected aggregate loss \(\times\) % unreported

• Caveat: doesn’t take into account if the aggregate is about to be pieced of not

7.8.1 Table M

Appendix discuss calculation with Table M

From paper appendix, to be included later…(Not crucial)

Need adjusted losses to determine ELG

\[\text{Adj Losses} = \underbrace{\dfrac{1 + 0.8 \cdot \chi}{1 - \chi}}_{\text{Adj Factor}} \times \mathrm{E}[\text{Unlimited Loss}]\]

Entry ratio:

\[\dfrac{\text{Agg Limit}}{\text{Expected Losses in Layer}}\]

Use entry ratio to lookup insurance charge and apply to the expected loss in layer to get the expected loss XS the aggregate