Abstract:
The article considers the problem of numerical estimation of functional from the solution of a system of non-linear Boltzmann type equations occurring in the stochastic kinetic model of asset price formation. This topic is relevant due to the constant increase in the volume of high-frequency trading at financial markets. This leads to the necessity to improve trading algorithms, taking into account the stochasticity of the price series parameters such as drift and volatility, as well as the behavior of traders during the trading session. The authors proposed an integral equation of the second kind associated with the linear multi-particle model of the behavior dynamics of a set of traders (vendors and buyers) at the exchange for the initial probabilistic price model. To estimate the functionals from the solution of the obtained equation, it is proposed to use the apparatus of the weighted Monte Carlo algorithms. Developed statistical algorithms will be applied to build the price forecast inside the trading session in real time mode. The combination of the short-term forecast based on the kinetic model and the
long-term forecast of price series based on the stochastic dynamic model will be the mathematical basis of the adaptive intellectual system. This system, based on historical and current market data, will automatically create personal financial recommendations.
Keywords:Boltzmann-type equation, Monte Carlo method, stock quotes order book, transaction rate, intellectual system.
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