We show that the problem of pricing the American put is equivalent to solving an optimal stopping problem. the optimal stopping problem gives rise to a parabolic free-boundary problem. We show there is a unique solution to this problem which has a lower boundary. We identify an integral equation...

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence, and are non-topological in nature. We give Storokhod representation results for two of these modes of convergence, and give applications to sufficient statistics and conditioned Markov...

An embedding of an arbitrary centred law [mu] in a Brownian motion (that is a stopping time T and a Brownian motion B such that (Bt)=[mu] and (Bt[Lambda]T; t[greater-or-equal, slanted]0) is found such that B*T has a law which dominates that of M*[tau], where the pair (M, [tau]) is any other ui...