Premium p definition
I am confused by the definition of "p" in the wiki and in Example 6.3. The wiki says:
"Let N be the per policy claim count random variable, m be the number of exposures, and ϕ be the ground-up claim frequency per exposure. Let Y be the claim size including ALAE. Then E[N]=mϕ is the expected claim count and the expected loss and ALAE for a policy is given by E[N]⋅E[Y]. The per policy pure premium is p=ϕ⋅E[Y]."
Why isn't p here "per exposure" instead of "per policy" since ϕ is per exposure frequency?
Following that, in Example 6.3, the solution seems to define p as E(N)*E(Y), which also seems to conflict with the p=ϕ⋅E[Y] formula here.
Comments
You're right, it should say per exposure rather than per policy. The wiki has been updated and we've clarified example 6.3, thanks.
Thanks!