Before revision:  We extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and show how to calculate it in terms of a coupled system of generalized Riccati equations.
After revision:  We extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and show how to calculate discounted complex moments by solving a coupled system of generalized Riccati equations.