A stochastic chartist–fundamentalist model of speculative asset dynamics in financial markets is developed. The model is represented by a stochastic delay-differential equation (SDDE). The SDDE is then solved using approximation and numerical Monte Carlo methods. The results show that for large time delays, the SDDE generates market-like stock price dynamics that reflect the memory effects of the time delay. The resultant dynamics agree with the empirical observation of the tendency of stock markets to deviate from pure random walk.
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Dibeh, G., Harmanani, H.M. A Stochastic Chartist–Fundamentalist Model with Time Delays. Comput Econ 40, 105–113 (2012). https://doi.org/10.1007/s10614-012-9329-8