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Chapter 4 Question 4.6

M

mcallist

Member
Hi,

Could someone please explain the substitution in this question and where the 5dy comes from?

Many thanks,
Tom
 
mcallist said:
Hi,

Could someone please explain the substitution in this question and where the 5dy comes from?

Many thanks,
Tom
Click to expand...

X is the random variable of total claim amount and Y is the random variable of claim amt. paid by the reinsurer. Here,
X~Gamma(a,L)
Retention limit is 80%, means the reinsurer is paying 20% proportion of each claim. So, Y= 0.20 X
Take the pdf of gamma dist. and substitute Y= 0.20X → X= 1/0.20 Y → X= 5Y
and so, dx= 5dy.
Try by yourself, you will get it.
 
Bharti Singla said:
X is the random variable of total claim amount and Y is the random variable of claim amt. paid by the reinsurer. Here,
X~Gamma(a,L)
Retention limit is 80%, means the reinsurer is paying 20% proportion of each claim. So, Y= 0.20 X
Take the pdf of gamma dist. and substitute Y= 0.20X → X= 1/0.20 Y → X= 5Y
and so, dx= 5dy.
Try by yourself, you will get it.
Click to expand...

Thanks a lot Bharti :)
 
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