Before revision:  By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which asset price moments do not explode at any time or explode at a given time.
After revision:  By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time.