Course 3, Nov 2001, #35

[KHLKL]

I hope someone can help me out on this. I don't understand the solution from SOA.

Why E(X) = E(X^1000)?

Thanks!

[Macroman]

the E(X^1000) is the symbol for limited expected value, meaning

E[max(X,1000)]

as would be the case of expectation of a random variable representing an insurance company's liability subject to a policy limit or retained maximum of 1000. Alternatively, it could represent the policyholder's responsibility on a policy with a deductible of 1000.

Note that in the SOA solution the carret is aligned lower than it appears in this text, since the SOA also uses the carret for exponents.

[mopete]

i think macroman made a slight typo E[X^1000] = E[ min (x,1000)]

[Macroman]

right, thanks...

[Elisha]

I thought this was one of the easiest last time - one of the few that I actually got right.

Since E[X ^ 1000] has F(1000)=1, E[X^1000] must be equal to E[X], then it is just (E[X^1000] - E[X^100])/(1 - F(100)), your basic mean excess loss formula. So (331 - 91)/(1 - .2) = 240/.8 = 300.

[phdmom]

Why E(X) = E(X^1000)?


If F(1000)=1, then X must be less than 1000, so X^1000 = X (and then E[X^1000] = E[X]).