Mathematics and Financial Economics

, Volume 5, Issue 3, pp 185–202 | Cite as

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

  • Igor V. Evstigneev
  • Thorsten Hens
  • Klaus Reiner Schenk-Hoppé
Article

Abstract

This paper introduces and analyzes an evolutionary model of a financial market with 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 investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.

Keywords

Evolutionary finance Risk-free asset Local stability Linearization Random dynamical systems 

JEL Classification

G11 G12 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Igor V. Evstigneev
    • 1
  • Thorsten Hens
    • 2
    • 3
  • Klaus Reiner Schenk-Hoppé
    • 3
    • 4
  1. 1.Economics Department, School of Social SciencesUniversity of ManchesterManchesterUK
  2. 2.Department of Banking and FinanceUniversity of ZurichZurichSwitzerland
  3. 3.Department of Finance and ManagementNHH–Norwegian School of EconomicsBergenNorway
  4. 4.Leeds University Business School and School of MathematicsUniversity of LeedsLeedsUK

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