Exam C小问题求救

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Aggregate losses S under an insurance policy follow a compound process with Poisson
frequency (mean = 5), and a severity distribution with moments  E[X ]=800 , and E[X^2]=2,080,000
You are given that  P[S>y]=0.025.  Find y.

是不是要用normal approximation?

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关键词：Exam C Exam 小问题 distribution Aggregate frequency insurance compound process follow

貌似是要用recursive formula做吧

i think should be normal approximation too. Claims frequency follows poisson, E(N)=V(N)=5. Severity is X. E(S)=E(N)E(X). V(S)=E(N)V(X)+E(X square)V(N)
then apply normal approximation with mean and standard deviation of S.  

alphazc 发表于 2012-2-26 13:12
i think should be normal approximation too. Claims frequency follows poisson, E(N)=V(N)=5. Severity  ...

agree wif u, but for Var(S), we can use Var (S) = E(N) * E(X^2) since it is compound poisson

junbin1125 发表于 2012-2-26 15:59
agree wif u, but for Var(S), we can use Var (S) = E(N) * E(X^2) since it is compound poisson

it should be E(N) *( 2E(X square)- E(X) square )

alphazc 发表于 2012-2-26 16:07
it should be E(N) *( 2E(X square)- E(X) square )

may i know where u get this formula?

alphazc 发表于 2012-2-26 13:12
i think should be normal approximation too. Claims frequency follows poisson, E(N)=V(N)=5. Severity  ...

juz noticed, V(S)=E(N)V(X)+E(X square)V(N) is wrong...
should be V(S)=E(N)*V(X)+E(X)^2*V(N)
you might want to check ur study manual again

but the question did not mention using "normal approximation". should i still assume that i can use normal approx?

psp-fifa-fan 发表于 2012-2-26 23:20
but the question did not mention using "normal approximation". should i still assume that i can use  ...

i dun think there is any other way to do it, since we dunno the distribution of severity function

junbin1125 发表于 2012-2-26 16:51
juz noticed, V(S)=E(N)V(X)+E(X square)V(N) is wrong...
should be V(S)=E(N)*V(X)+E(X)^2*V(N)
you  ...

opps~ im noob >.< thank you so much.