Gambler’s ruin problem and bi-directional grid constrained trading and investment strategies


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Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically until now, are relatively new in the world of financial markets and have the ability to out-perform many other trading algorithms in the short term but will almost surely ruin an investment account in the long term. Whilst the Gambler’s Ruin Problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required to solve the grid trading problem (GTP), i.e. a form of BGC financial markets strategies, and how it can deliver greater return on investment (ROI) for the same level of risk. A novel theorem of GTP is derived, proving that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. These results not only can be studied within mathematics and statistics in their own right, but also have applications into finance such as multivariate dynamic hedging, investment funds, trading, portfolio risk optimization and algorithmic loss recovery. In today’s uncertain and volatile times, investment returns are between 2%-5% per annum, barely keeping up with inflation, putting people’s retirement at risk. BGC and GTP are thus a rich source of innovation potential for improved trading and investing.

Aldo Taranto was supported by an Australian Government Research Training Program (RTP) Scholarship. The authors would like to thank A/Prof. Ravinesh C. Deo and A/Prof. Ron Addie of the University of Southern Queensland for their invaluable advice on refining this paper.

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    • Figure 1. Three discrete random walks in GRP
    • Figure 2. GTP ruin accumulation process
    • Figure 3. GRP transition probabilities of with
    • Figure 4. GTP transition probabilities of with
    • Figure 5. 2-sample GRP simulations
    • Figure 6. Multiple GRP simulations
    • Figure 7. 2-sample GTP simulations
    • Figure 8. Multiple GTP simulations
    • Figure 9. Sample Positive Growth Path of a Grid Trader in MT4
    • Conceptualization
      Aldo Taranto, Shahjahan Khan
    • Data curation
      Aldo Taranto
    • Formal Analysis
      Aldo Taranto
    • Investigation
      Aldo Taranto
    • Methodology
      Aldo Taranto, Shahjahan Khan
    • Project administration
      Aldo Taranto
    • Resources
      Aldo Taranto, Shahjahan Khan
    • Software
      Aldo Taranto
    • Validation
      Aldo Taranto
    • Visualization
      Aldo Taranto
    • Writing – original draft
      Aldo Taranto
    • Writing – review & editing
      Aldo Taranto, Shahjahan Khan
    • Supervision
      Shahjahan Khan