PDA

View Full Version : Course 3, Nov 2001, #35

KHLKL
05-11-2002, 08:17 PM
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
05-11-2002, 09:35 PM
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
05-12-2002, 12:10 AM
i think macroman made a slight typo E[X^1000] = E[ min (x,1000)]

Macroman
05-12-2002, 12:15 AM
right, thanks...

Elisha
05-12-2002, 02:56 AM
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
05-12-2002, 11:53 AM
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]).