Exponentially affine martingales, affine measure changes and exponential moments of affine processes

We consider local martingales of exponential form M = e X or E ( X ) , where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M 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.