martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed … given, fi xed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value … of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of …

equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the fi rst kind to the … existence of an equivalent local martingale deflator for the set of non negative wealth processes …

decomposed into a sum with two opportunity processes L± appearing as coefficients. The martingale optimality principle translates …, stochastic control ; semimartingales ; BSDEs ; martingale optimality principle ; opportunity process ; E-martingales ; linear …

finance ; variance-optimal martingale measure …

An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R … equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical … only a local integrability requirement. sigma-martingale ; equivalent martingale measures ; Jacod decomposition …

The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag …

A P-sigma-martingale density for a given stochastic process S is a local P-martingale Z>0 starting at 1 such that the … product ZS is a P-sigma-martingale. Existence of a P-sigma-martingale density is equivalent to a classic absence … there exists a P-sigma-martingale density for S. Can we find another P-sigma-martingale density for S having some extra …

characterisations of our concepts in terms of martingale properties. A key new feature is that as one expects, “properly anticipated …