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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset
Organization Unit
Authors
  • Igor V Evstigneev
  • Thorsten Hens
  • Klaus Reiner Schenk-Hoppé
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Journal Title Mathematics and Financial Economics
Publisher Springer
Geographical Reach international
ISSN 1862-9660
Volume 5
Number 3
Page Range 185 - 202
Date 2011
Date Annual Report 2011
Abstract Text This paper introduces and analyzes an evolutionary model of a financial marketwith a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investmentstrategy in the evolutionary model with a risk-free asset is derived, extending previousresearch. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.
Digital Object Identifier 10.1007/s11579-011-0056-z
Other Identification Number merlin-id:6849
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Additional Information The original publication is available at www.springerlink.com