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


Hens, Thorsten; Schenk-Hoppé, Klaus Reiner; Evstigneev, Igor V (2010). Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset. Swiss Finance Institute Research Paper 10-36, University of Zurich.

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, Pirogov and Schenk-Hoppé, Proceedings of the American Mathematical Society 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.

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, Pirogov and Schenk-Hoppé, Proceedings of the American Mathematical Society 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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2010
Deposited On:05 May 2014 15:59
Last Modified:15 Aug 2017 08:51
Series Name:Swiss Finance Institute Research Paper
Official URL:http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1669962
Other Identification Number:merlin-id:6003

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