Mahler 2 - Retro Rating 1997 ELFs

Question 1

Two phenomena that would affect excess ratios that are not being considered

Answer 1

1. loss development may be different for different sizes of loss
2. there is a “dispersion” effect
   Assume we have two claims of $1 million each tat are expected on average to develop by 10%. It makes a difference whether we’ll have two claims each at $1.1M, or one claim at $1M, and one claim at $1.2M. The ratio excess of $1.1M will differ in two cases.

Question 2

Impact of simple Dispersion

Answer 2

Raises excess ratio higher limits, alter for lower limits

Higher CV, larger the impact on the excess ratio

Question 3

Impact of Gamma dispersion

Answer 3

1. particular significant impact on very high limits, esp if variance is large
2. allows extreme values with small probability

Question 4

Gamma(s,l) loss divisor applied to expo(lemda) loss distribution

Answer 4

Result is Pareto (s, l/lemda)

Question 5

Gamma loss divisor applied to pareto losses

Answer 5

As shape parameter of Pareto (alpha) gets smalls => loss has heavier tail and impact of dispersion increase

As CV of gamma increase, impact of dispersion increase