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Finance theory applications of learning, evolution and self-organization

University of British Columbia

This thesis investigates stochastic adaptive learning and contrasts models of adaptive individuals with models that assume complete and unbounded rationality. In this thesis, individuals follow rules of thumb which are developed by adopting or copying successful rules, abandoning unsuccessful ones and occasionally creating novel rules. In fixed environments, these learning algorithms differ only slightly from complete rationality Bayesian approaches. However, in situations where an individual’s utility depends on the behaviour of other individuals, a co-evolutionary environment, the prediction of adaptive learning models can differ markedly from traditional complete rationality models. In the first section of the thesis interaction between individuals’ decisions is limited and direct. People face their neighbours in a repeated prisoner’s dilemma. A genetic algorithm, used as an example of a stochastic adaptive learning process, is developed in Chapter 2. The rate of learning in the algorithm is controlled by altering the number of individuals obtaining new strategies in a generation. In the infinitely repeated game the learning rate affects the equilibrium level of payoffs (ie. affects which equilibria are selected). In the finitely repeated game the learning rate determines whether or not the system converges to the unique Nash equilibrium. Chapter 3 considers a similar model analytically yielding analogous results. The second portion of the thesis investigates stochastic adaptive learning in a non-strategic yet co-evolutionary environment. This section develops an asymmetric information, one-period, single risky asset portfolio choice model based on Grossman and Stiglitz (1980). The main finding of these three chapters is that the appropriateness of the rational expectations (or complete rationality) equilibrium depends upon the level of noise in the economy (in the form of noise traders) relative to the level of experimentation in the individual’s learning processes. The discussion of this relationship begins in Chapter 4 by constructing a learning process which converges to the rational expectations equilibrium and concludes with a discussion of the stability of the Grossman-Stiglitz equilibrium to an adaptive learning process where experimentation does not vanish. Chapter 5 develops a deterministic representation of a stochastic adaptive learning process to formally develop the link between noise trading, experimentation and the Grossman-Stiglitz equilibrium. Finally, Chapter 6 demonstrates the stability result in a more general environment using a genetic algorithm as an example of a stochastic adaptive process.

Thesis/Dissertation

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2009-04-24

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http://hdl.handle.net/2429/7553

Business Administration

University of British Columbia

UBCV

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