Abstract
This paper studies the behavior of the exchange rate in Kareken and Wallace (1981)'s model under the genetic algorithm adaptation with agents having long memory. The simulation results show that, if agents have full memory, the average portfolio fraction will converge, and the initial equilibrium that it converges to is history dependent. Under the lasting evolutionary pressure of the noise trader, the market will eventually drift from one equilibrium to another, and asymptotically will converge to the neighborhood of an equilibrium with agents putting their savings equally into two currencies. If the agents do not have full memory, the foreign exchange market will show periodic crisis. Before and after a market crises, the average portfolio fraction will converge to different stationary equilibria. A mean difference equation of the average portfolio fraction is also given to describe the dynamics of the model.
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Notes
The reason we set the memory length at 400 is that we want to give GA enough time to settle down. However, if this number is too big, huge numbers of iterations will be needed in order to show the whole picture of the dynamics.
Same as other simulations, in both experiments, the size of the candidate set is fixed at one half of the size of the strategy population.
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The author thanks Jasmina Arifovic and Robert Jones for their helpful comments and suggestions. Support by the funding of “211 Project of UIBE” is gratefully acknowledged.
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Xu, Y. The behavior of the exchange rate in the genetic algorithm with agents having long memory. J Evol Econ 16, 279–297 (2006). https://doi.org/10.1007/s00191-005-0006-0
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DOI: https://doi.org/10.1007/s00191-005-0006-0