Chpater 8 Question 8.5

I don't understand why the variance of the insurer profit, which is equal to the premium charged less the risk claim, is the same as the variance of the total claim.
Assuming that : insurance profit (without reins) is : E(1.2*S-S) then Variance is : 0.2^2*Var(s) which is not equal to Var(S).
We have the same logic when assuming reinsurance.

the reason mentioned in the solution is since only the claims are random.

Please any help?

 

Hi
I also have this doubt. What I think its reason, is in the pic below. Check this once. But I'm not much sure about it, need to confirm. Tutors please rectify if I am wrong.

 

I understand what you say,

You mean that the premium is considered as "known value" as we can apply one of the basic properties of the var which is var(x+C)=Var(x)

This is confusing because when you intend the exercise you suppose the premium being 1.2Si and not 600Mu .

I also understand from you description that the reinsurance premium and the aggregate claim paid are "known numbers" as we also be able to assume that the variance of the insurer profit be equal to the variance of the aggregate net claim paid by the insurer after reins.

 

I have taken Premium as 1.2×E(S) not 1.2×Si. E(S) should be fixed.
Yes, I think we are using this property here:
Var(Profit)=Var[1.2×E(S) - Si]
= 0+(-1)²Var(Si)
= Var(Si)
where Si is the aggregate claim amount paid by the insurer.
But still need to verify.

 

Tutors please suggest, Is it the right way to prove this.(i.e. Variance of Profit is same as Variance of aggregate claims amount paid by insurer)?

 

who is Tutors?

 

I meant to say ActEd Tutors/ Staff Members

 

Yes this is correctly interpreted.

 

Thankyou Varsha.

 

Okay.Thankyou sir.