A prototype model of speculative dynamics with position-based trading

The paper extracts a prototype asset pricing model from the literature where a market maker adjusts prices in response to order imbalances and the strategies of fundamentalists and chartists are position-based, that is, the two groups are specified in terms of their desired holdings. The deterministic formulation of the model leads to a neutral delay-differential equation of the price, whose mathematical analysis is non-standard and may be of independent interest. The stability conditions are nevertheless quite analogous to the order-based Beja-Goldman model. The effects of parameter variations are also studied in a stochastic setting, where special emphasis is put on the misalignment between price and the time-varying fundamental value, the market maker's risk aversion, and the differential profits of fundamentalists and chartists.