Let X be exponential, and u(x) = e x . Show that for the certainty equivalent c(X), we have as E{X}0, that is, c(X) E{X}

Let X be exponential, and u(x) = −e^−βx. Show that for the certainty equivalent c(X), we have

as E{X}→0, that is, c(X)≈ E{X} if E{X} is small. Interpret it considering u(x) for small x’s.