Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies

Details Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies

2011-02-04

arxiv.org/abs/1102.1713v2

Economy

Quantitative Finance

General Finance

7 pages, 6 figures

Scientific paper

Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter $\epsilon$. We demonstrate, that within Gaussian noise, the variance of the resulting wealth distribution will significantly decrease, and the equilibrium state is reached faster than in the case of a uniform distributed $\epsilon$ parameter. Also, we show that the system with Gaussian noise strongly resembles a deterministic system which is solved by means of a Z-Transform based technique.

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