A characterization of the martingale property of exponentially affine processes

We consider local martingales of exponential form M=eX or E(X)E(X) where XX denotes one component of a multivariate affine process in the sense of Duffie et al. (2003) [8]. By completing the characterization of conservative affine processes in [8, Section 9], we provide deterministic necessary and sufficient conditions in terms of the parameters of XX for MM to be a true martingale.