  We investigate which jump-diffusion models are convexity preserving. The
study of convexity preserving models is motivated by monotonicity results for
such models in the volatility and in the jump parameters. We give a necessary
condition for convexity to be preserved in several-dimensional jump-diffusion
models. This necessary condition is then used to show that, within a large
class of possible models, the only convexity preserving models are the ones
with linear coefficients.
