ST8 - CH15 ILF formula

[Nnè London]

Pg 26 of CH15 gives the formula of how to work out the expected layer loss cost using C(L) = C(B)(ILF(L+D)-ILF(D)). However Q15.7 does not seem to use that formula and I am confused as to why the solution to the question shows a division of ILFs rather than subtraction as per the formula. Moving on to pg 29, another formula is given which is:
C(L)=C(l)(((ILD(L+D)-ILF(D))/ILF(L)), where C(l) is the expected loss cost of the original limit.

Can anyone shed any light on the difference between the basic limit and the original limit and when to use the different formulae?

Thanks

 

[Duncan Brydon]

Pg 26 of CH15 gives the formula of how to work out the expected layer loss cost using C(L) = C(B)(ILF(L+D)-ILF(D)). However Q15.7 does not seem to use that formula and I am confused as to why the solution to the question shows a division of ILFs rather than subtraction as per the formula.

In question 15.7, there is no deductible D so we do not need the formula on page 26. Look back to the formulae and notation on page 24 instead. In Question 15.7, b=£100,000 and x=£1,000,000.

Moving on to pg 29, another formula is given which is:
C(L)=C(l)(((ILD(L+D)-ILF(D))/ILF(L)), where C(l) is the expected loss cost of the original limit.

Can anyone shed any light on the difference between the basic limit and the original limit and when to use the different formulae?

Page 29 is discussing reinsurance. The original limit refers to any limit in the underlying policy written by the cedant. When we define an ILF, it is always with respect to some basic limit b. ILF(x) is the ratio of expected losses (to the reinsurer) if a limit x is used for the (reinsurance) policy to the expected losses if limit b is used.

I hope this helps.
Good luck.