Question

6. In year 2019, claim amounts follow a Pareto distribution with parameters a = 3 and = 800. The annual inflation rate is 8%. A franchise deductible of 300 will be implemented in 2020. Calculate the loss elimination ratio of the franchise deductible in 2020. (Note: Theorem 8.5 only holds for ordinary deductible, so it is not applicable here. You should start with the definition of the loss elimination ratio for franchise deductible. Modify Definition 8.4 by replacing the word "ordinary" by "franchise" and proceed from there.)

please write legible

Answer 1

Loss Elimination Ratio :- - Loss Elimination ratio it is the ratio in recluction in estimated payment with franchise deductible to estimate poated estimated payment without deductible Given facts, Soo Inflation rate (n) = 8% franchise decertible (d)= 300 Computation loss Elimination Rato CLER): General LER with oxloary deductible is. FCX deductible is But LER with franchise -ECx7 - Pr (x >d) d) ЕСх)

son parameter thata (0) with inflation is - 800x640,08) - 86 (1,08) 864 =) لا (2) ( 864 (3ect 69 ( 2 1162 = 3 ( = 05sec) (موله) لثه - = 193,985 ] = ا-3 ح 669 = - خدع و 45 -

Pr. (x>d) - Pr. Cx2300) -1.864 864 +300) (0.748268)} & 0.40896 RCxd) Pr CX300)(80) no 40896 x 300 122.688 so, LER = [[[x] - P(x >d ) d] - (193.985 - 122.688) 432

71.297 432 16.50% This means, by introducing of 300 we can eliminate franchise decluctible 16.50% of losses.