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Analytic solutions in a continuous-time financial market model

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Document pages: 14 pages

Abstract: We propose a heterogeneous agent market model (HAM) in continuous time. Themarket is populated by fundamental traders and chartists, who both use simplelinear trading rules. Most of the related literature explores stability, pricedynamics and profitability either within deterministic models or by simulation.Our novel formulation lends itself to analytic treatment even in the stochasticcase. We prove conditions for the (stochastic) stability of the price process,and also for the price to mean-revert to the fundamental value. Assumingstability, we derive analytic formulae on how the population ratios influenceprice dynamics and the profitability of the strategies. Our results suggestthat whichever trader type is more present in the market will achieve higherreturns.

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