Hi all In chapter-4, under XOL reinsurance, we have two types of distribution of claims paid by reinsurer- conditional and unconditional. I am getting confuse in questions which distribution is to be used while calculating mean claim amount paid by reinsurer. If the qus. is unclear about it then which dist. is to be used? Please anyone help! Thanks
In any question,Distribution of X=Amt of Claims/losses that arises is given to us(Which follows either pareto or logNormal distribution) Now this amount of claim is paid by insurer(say Y) and reinsurer(say z) .so E(X)=E(Y)+E(Z). When M is Retention limit in XOL reinsurance,we find Expected value of Z as expected value of X within the limits M<X<inf.And that of insurer =E(X)-E(Z). Now this was the case of Unconditional reinsurance. In Case of conditional reinsurance,reinsurer considers only those claims in which it is involved i.e E(z)=E(Z|X>M).Here we can find this as E(Z)/P(X>M) or we can drive the conditional pdf of Z which has same distribtn of X with differnt/same parameter and then can find its mean.
Thanks for explaining Varsha but , in questions how do we know which distribution mean they are asking- conditional or unconditional? Like- in some qus. it is clearly stated that 'find the mean of claim amount paid by reinsurer in which he is involved'. Then we will use conditional distribution. But if it is unclear, then which distribution should be used?
In some questns,proportion of claims in which reinsurers is involved is asked,there following questn wants to know conditional mean amt paid by reinsurer...while in others where both insurer and reinsurer's mean is asked we find unconditional mean.This is what i can recall..do refer to some questn which u find difficult to chose between two,i can then help explain better.
Hey, here are two questions in which I'm not getting the difference. In sept, 2002 qus. part(ii)(a) : Here is a policy excess present, so the insurer will play the same role as reinsurer in case of XOL. The qus. is asking to calculate the expected claim size payable by the insurer. And they have used CONDITIONAL distribution here. Qus of sept,2006 part(iii): Here, Xr is the claim amount paid by the reinsurer. And while calculating E(Xr) UNCONDITIONAL distribution is used. Please explain. Thanks
Yes both are correct. You see policy excess and XOL reinsurance works on different principles.For policy excess ,if you claim more than say 100 then only insurer will pay or else you have to bear your only expnse(you cant claim for very some amount ),so in this case its always conditional that insurer will pay only if its exceeds policy excess.Whereas in case of reinsurance sometimes reinsurers considers mean amt paid on all claims even though it actually pays claims for few(Unconditional) and sometimes its considers mean amt paid on the claims in which it is involved only(in that case we use conditional). So in Sep2002 policy excess is consider conditional,and in Sep 2006 its asked for mean amt of reinsurer and insurer on all claims so unconditional.
