Asset flow model for a homogeneous group of investors: High-frequency trading limit

Deterministic and stochastic asset flow models have been designed to study the effects of behavioral components on market dynamics. These successful in explaining mechanisms behind price overshoots, oscillations, reversals, liquidity- value-induced bubbles flash crashes. While these are originally nonlinear, we demonstrate here that, case a consisting homogeneous group investors with identical trading sentiments, natural modifications response functions yield version that can be represented by linear dynamical system across entire state space system. We show this exhibits all types behavior, just like nonlinear version, while also having benefit being explicitly integrable even time-varying parameters. present limiting model corresponds fast trading, which is appropriate for modern electronic markets, provide examples illustrating differences variability intrinsic value shares or liquidity.