loss elimination ratio for franchise deductible

[goodluck]

How to find loss elimination ratio for franchise deductible? Particularly, they ask for in #33. Thanks.

http://casact.org/admissions/studyto...am3/fall05.pdf

[ActuaryToBe]

With a normal deductible: LER = E[X^d]/E[X]

So, for a franchise deductible, LER = (E[X^d] - Pr(X>d) d)/E[x],
because for a franchise deductible, if X>d, then no deductible is applied. So, since E[X^d] includes dedudctibles of amount d for X>d, you want to subtract those from E[X^d] (i.e. subtract Pr(X>d) d).

Also, note that this is a Pareto, with parameter theta = @ = 800 (without applying inflation) and alpha = a = 3.

Applying inflation = @ = 800(1.08) = 864

So, using the formulas in the tables:
E[X^d] = (864/2)(1-(864/(864+300))^2) = 193.98
E[X] = 864/2 = 432
Pr(X>300) = (864/(864+300))^3 = 0.40896
Pr(X>300) (300) = 300(0.40896) = 122.69

So LER = (193.98-122.69)/432 = 16.5%, which corresponds to B.

[goodluck]

Originally Posted by ActuaryToBe

With a normal deductible: LER = E[X^d]/E[X]

So, for a franchise deductible, LER = (E[X^d] - Pr(X>d) d)/E[x],
because for a franchise deductible, if X>d, then no deductible is applied. So, since E[X^d] includes dedudctibles of amount d for X>d, you want to subtract those from E[X^d] (i.e. subtract Pr(X>d) d).

Also, note that this is a Pareto, with parameter theta = @ = 800 (without applying inflation) and alpha = a = 3.

Applying inflation = @ = 800(1.08) = 864

So, using the formulas in the tables:
E[X^d] = (864/2)(1-(864/(864+300))^2) = 193.98
E[X] = 864/2 = 432
Pr(X>300) = (864/(864+300))^3 = 0.40896
Pr(X>300) (300) = 300(0.40896) = 122.69

So LER = (193.98-122.69)/432 = 16.5%, which corresponds to B.

Thanks

[NewTubaBoy]

I know you guys don't have Lee Diagrams on your exam, but I've always said that they're so helpful in doing these type of problems. I know it's very close to the exam, and you've got other stuff to study... but if you have a Mahler guide around he provides them for CAS people. If you look over it it would help clarify this in a really cool visual way.