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Title: Random dynamics in financial markets
Author: Bektur, Cisem
ISNI:       0000 0004 2724 024X
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2012
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We study evolutionary models of financial markets. In particular, we study an evolutionary market model with short-lived assets and an evolutionary model with long-lived assets. In the long-lived asset market, investors are allowed to use general dynamic investment strategies. We find sufficient conditions for the Kelly portfolio rule to dominate the market exponentially fast. Moreover, when investors use simple strategies but have incorrect beliefs, we show that the strategy which is "closer" to the Kelly rule cannot be driven out of the market. This means that this strategy will either dominate or at least survive, i.e., the relative market share does not converge to zero. In the market with short-lived assets, we study the dynamics when the states of the world are not identically distributed. This marks the first attempt to study the dynamics of the market when the probability of success changes according to the relative shares of investors. In this problem, we first study a skew product of the random dynamical system associates with the market dynamics. In particular, we compute the Lyapunov exponents of the skew product. This enables us to produce a "surviving" investment strategy, i.e., the investor who follows this rule will dominate the market or at least survive. All the mathematical tools in the thesis lie within the framework of random dynamical systems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Evolutionary finance ; Random dynamical systems ; Kelly rule