International audienceGiven (M_t)_{t∈ℜ_+} and (M*_t)_{t∈ℜ_+} respectively a forward and a backward exponential martingale with jumps and a continuous part, we prove that E [Φ(M_tM*_t)] is non-increasing in t when Φ is a convex function, provided the local characteristics of the stochastic logarithms of (M_t)_{t∈ℜ_+} and of (M*_t)_{t∈ℜ_+} satisfy some comparison inequalities. As an application, we deduce bounds on option prices in markets with jumps, in which the underlying processes need not be Markovian. In this setting the classical propagation of convexity assumption for Markov semigroups (see for instance [El Karaoui, Jeanblanc and Shreve, Math. Finance, vol. 8, 1998]) is not needed
