Chen, Ying (contributor); Härdle, Wolfgang (contributor); … - 2005
integration depends only on the exponential part, it holds also that
integraldisplay ∞
0
zneuzg(z)dz =
integraldisplay ∞
0
∂n
∂un …
holds for every t > 0,
E[euy] = E[eu|x|γ] = E[eu|x|γ1(|x| ≤ t)]+E[eu|x|γ1(|x| > t)]
≤ eutγ +E[e|x|utγ−1I(|x| > t)], (23 …e−(α−β−utγ−1)t
where C1,C2 > 1.
28
Consequently for t ≥ t0,
E[eu|t|γ−1x1(|x| > t)] =
integraldisplay ∞
t
eutγ−1xf …