Without some supplemental conditions on T , the problem of Skorokhod embedding is trivial. Suppose W is a Brownian motion with respect to a filtration {Ft} satisfying the usual conditions. Suppose Y...

Without some supplemental conditions on T , the problem of Skorokhod embedding is trivial. Suppose W is a Brownian motion with respect to a filtration {Ft} satisfying the usual conditions. Suppose Y is a finite random variable and suppose h is a real-valued function such that h(W₁) has the same law as Y.

(1) Show that if
  then WT and Y have the same law.

(2) Give an example of a mean zero random variable Y with finite variance such that if T is defined as in (1), then E T = ∞.