Exponentially affine martingales, affine measure changes and exponential moments of 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. We give a weak sufficient criterion for MM to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two given affine processes. As a second application, we study whether the exponential moments of an affine process solve a generalized Riccati equation.