Limit theorems in financial market models |
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Authors: | Koji Kuroda |
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Institution: | a Graduate school of Integrated Basic Sciences, Nihon University, Tokyo, Japan b Graduate school of Humanities and Social Sciences, Okayama University, Okayama, Japan |
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Abstract: | Invariance principle states that a scaled simple random walk converges to the standard Brownian motion.In this article, we present a discrete time stochastic process, which reflects a microstructure of market dynamics, and prove a convergence to a scaling limit process with a drift term and a jump term. These terms are derived from a macroscopic condition on volumes traded in some time intervals. The mathematical tools for obtaining our results are Dobrushin-Hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics. |
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Keywords: | Continuous double auction Drift coefficient Jump process Cluster expansion Dobrushin-Hryniv theory |
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