Laplace transform analysis of a multiplicative asset transfer model

Details Laplace transform analysis of a multiplicative asset transfer model Laplace transform analysis of a multiplicative asset transfer model

2010-04-29

arxiv.org/abs/1004.5169v1

Physica A 389 (2010) 2782-2792

Economy

Quantitative Finance

General Finance

Scientific paper

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of $f\in(0,1)$. The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

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