Stability analysis of Riccati differential equations related to affine diffusion processes
This paper studies a class of generalized Riccati differential equations associated with canonical affine diffusion processes arising in financial econometrics and branching processes and then shows several properties of the system and the blow-up time. The boundaries of stability regions is characterized, which can be expressed as unions of stable sub-manifolds of equilibria on the stability boundaries under the assumption that every bounded trajectory converges to an equilibrium. The asymptotic behavior of the blow-up time is studied, the blow-up regions of the system are defined via the blow-up times, and the boundaries of blow-up regions are the level sets of the blow-up times. The implications of applying the obtained results to affine diffusions and to option pricing theory are also discussed.
scientific article; zbMATH DE number 5669052
scientific article