Stability of Sigma-Martingale Densities in L log L Under an Equivalent Change of Measure

An equivalent !-martingale measure (E!MM) for a given stochastic process Sis a probability measure R equivalent to the original measure P such that S isan R-!-martingale. Existence of an E!MM is equivalent to a classical absenceof-arbitrage property of S, and is invariant if we replace the reference measureP with an equivalent measure Q. Now suppose that there exists an E!MM Rfor S such that the density dRdP is in L logL(P). Does this existence propertyalso remain invariant if we replace P by some equivalent Q? We prove thatthe answer is Yes if one imposes instead of a global only a local integrabilityrequirement.[...]