= Power payoff static call representation
{title2=$s^{1+\varepsilon}=\varepsilon(1+\varepsilon)\int_0^\infty K^{\varepsilon-1}(s-K)_+\,dK$}
For $s\ge0$ and $\varepsilon>0$, integrate over $0\le K\le s$ to obtain the displayed identity. <Tonelli theorem> then expresses the moment of a nonnegative random variable as the same integral of expected call payoffs, even when the moment is infinite. This is a static representation across strikes rather than a dynamic <replicating strategy> in a restricted finite-asset market.
Back to article page
