Abstract
We study a class of generalized Riccati differential equations associated with affine diffusion processes. These diffusions arise in financial econometrics and branching processes. The generalized Riccati equations determine the Fourier transform of the diffusion's transition law. We investigate stable regions of the dynamical systems and analyze their blow-up times. We discuss the implication of applying these results to affine diffusions and, in particular, to option pricing theory.
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