Research Article Open Access

Application of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic Trading

Aldo Taranto1 and Shahjahan Khan1
  • 1 University of Southern Queensland, Australia

Abstract

Bi-directional Grid Constrained (BGC) Stochastic Processes (BGCSP) become more constrained the further they drift away from the origin or time axis are examined here. As they drift further away from the time axis, then the greater the likelihood of stopping, as if by two hidden reflective barriers. The theory of BGCSP is applied to a trading environment in which long and short trading is available. The stochastic differential equation of the Grid Trading Problem (GTP) is proposed, proved and its solution is simulated to derive new findings that can lead to further research in this area and the reduction of risk in portfolio management.

Journal of Mathematics and Statistics
Volume 17 No. 1, 2021, 22-29

DOI: https://doi.org/10.3844/jmssp.2021.22.29

Submitted On: 23 November 2020 Published On: 6 March 2021

How to Cite: Taranto, A. & Khan, S. (2021). Application of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic Trading. Journal of Mathematics and Statistics, 17(1), 22-29. https://doi.org/10.3844/jmssp.2021.22.29

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Keywords

  • Grid Trading
  • Random Walks
  • Probability of Ruin
  • Stochastic Differential Equation
  • Bi-Directional Grids
  • Trending Grids
  • Mean Reversion Grids