Motivated by a hedging problem in mathematical finance, El Karoui and Quenez [7] and Kramkov [14] have developed optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We investigate the general structure of such optional...

Let I be a countable index set, and let P be a probability measure on C[0, 1]I such that the coordinate process satisfies an infinite-dimensional stochastic differential equation dX = dW+b(X,t)dt. In contrast to the finite-dimensional case, the time reversed process cannot always be described by...