We consider the problem of a trustee faced with investing a sum of money, the interest from which will be received by one party (the life-tenant) during his lifetime while the capital will go to another party (the survivor) on the death of the life-tenant. We assume mat there are "n"+ 1 assets...

We establish necessary and sufficient conditions for an H-martingale to be representable with respect to a collection, of local martingales. "M" H("P") is representable if and only if "M" is a local martingale under all p.m.'s "Q" which are "uniformly equivalent" to "P" and which make all the...

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...