Stability analysis of Riccati differential equations related to affine diffusion processes
type: Item
instance of: scholarly article
title: Stability analysis of Riccati differential equations related to affine diffusion processes
zbMATH Open document ID: 1203.34072
author: Kyoung-Kuk Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-02-12T00:00:00Z
review text: 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.
reviewed by: Meng Fan
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 5669052
zbMATH Keywords: periodic solution
zbMATH Keywords: Riccati differential equations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.11.020
OpenAlex ID: W1989259686
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DOI: 10.1016/J.JMAA.2009.11.020
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description: scientific article; zbMATH DE number 5669052