Locally Ф-integrable σ-martingale densitiesfor general semimartingales

A --martingale density for a given stochastic process is a local -martingale starting at 1 such that the product is a --martingale. Existence of a --martingale density is equivalent to a classic absence-of-arbitrage property of , and it is invariant if we replace the reference measure with a locally equivalent measure . Now suppose that there exists a --martingale density for . Can we find another --martingale density for having some extra local integrability under ? We show that the answer is always positive for one part of that we identify, and we show that the complete answer depends in a precise quantitative way on the local integrability of the drift-to-jump ratio of the remaining ‘jumpy’ part of . Our proofs provide in addition new ideas and results in infinite-dimensional spaces.