Gambler’s ruin problem and bi-directional grid constrained trading and investment strategies
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Author(s)Aldo TarantoLink to ORCID Index: https://orcid.org/0000-0001-6763-4997
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Shahjahan KhanLink to ORCID Index: https://orcid.org/0000-0002-0446-086X
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DOIhttp://dx.doi.org/10.21511/imfi.17(3).2020.05
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Article InfoVolume 17 2020, Issue #3, pp. 54-66
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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.
Acknowledgement(s)
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.
- Keywords
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JEL Classification (Paper profile tab)G11, G14, G17
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References35
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Tables0
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Figures9
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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
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- Admiral Markets. (2017). Forex Grid Trading Strategy Explained.
- Ahmed, U. (2017). How Forex Brokers Went Bankrupt Overnight amid EURCHF Flash Crash.
- Biagini, F., Guasoni, P., & Pratelli, M. (2000). Mean-Variance Hedging for Stochastic Volatility Models. Mathematical Finance, 10, 109-123.
- Czichowsky, C., Muhle-Karbe, J., & Schachermayer, W. (2012). Transaction Costs, Shadow Prices, and Connections to Duality.
- Davis M., & Norman A. (1990). Portfolio Selection with Transaction Costs. Mathematics of Operations Research, 15, 676-713.
- De Moivre A. (1712). De Mensura Sortis, Seu, de Probabilitate Eventuum in ludis a Casu Fortuito Pendentibus. Philosophical Transactions, 27, 213-264.
- Dumas, B., & Luciano, E. (1991). An Exact Solution to a Dynamic Portfolio Choice Problem Under Transaction Costs. Journal of Finance, 46(2), 577-595.
- DuPloy, A. (2008). The Expert4x, No stop, Hedged, Grid Trading System and The Hedged, Multi-Currency, Forex Trading System.
- DuPloy, A. (2010). Expert Grid Expert Advisor User’s Guide. September 21.
- Edwards, A. (1983). Pascal’s Problem: The ‘Gambler’s Ruin’. International Statistical Review. Revue Internationale de Statistique, 51(1), 73-79.
- El-Shehawey, M. (2000). Absorption Probabilities for a Random Walk Between Two Partially Absorbing Boundaries. Journal of Physics A: Mathematical and General, 33(49), 9005-9013.
- Feller, W. (1968). An Introduction to Probability Theory and Its Applications, 1 (3rd ed.). Wiley International Publishing.
- Fleming, W., & Hernández Hernández, D. (2003). An Optimal Consumption Model with Stochastic Volatility. Finance and Stochastics, 7(2), 245-262.
- Forex Strategies Work (2018). Grid Trading Strategy.
- Guasoni, P., & Muhle-Karbe, J. (2012). Portfolio Choice with Transaction Costs: A User’s Guide.
- Harris, M. (1998). Grid Hedging Currency Trading.
- King, J. (2010). ForexGridMaster v3.01 Manual.
- King, J. (2015). ForexGridMaster 5.1 Advanced Manual. February 5.
- Kmet, A., & Petkovssek, M. (2002). Gambler’s Ruin Problem in Several Dimensions. Advances in Applied Mathematics, 28(2), 107-118.
- Lefebvre, M. (2008). The Gambler’s Ruin Problem for a Markov Chain Related to the Bessel Process. Statistics & Probability Letters, 78(15), 2314-2320.
- Lengyel, T. (2009a). Gambler’s Ruin and Winning a Series by m Games. Annals of the Institute of Statistical Mathematics, 63(1), 181-195.
- Lengyel, T. (2009b). The Conditional Gambler’s Ruin Problem with Ties Allowed. Applied Mathematics Letters, 22(3), 351-355.
- Merton, R. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, 373-413.
- Mitzenmacher, M., & Upfal, E. (2005). Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 298.
- Muhle-Karbe, J., & Liu, R. (2012). Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints.
- Oksendal, B. (1995). Stochastic Differential Equations: An Introduction with Applications. New York: Springer.
- Pukthuanthong-Le, K., Levich, R., & Thomas, III L. (2007). Do Foreign Exchange Markets Still Trend? Journal of Portfolio Management, 34, 114-118.
- Rocha A., & Stern, F. (2004). The Asymmetric n-Player Gambler’s Ruin Problem with Equal Initial Fortunes. Advances in Applied Mathematics, 33(3), 512-530.
- Rogers, L., & Stapleton, E. (2002). Utility Maximisation with Time-Lagged Trading. Computational Methods in Decision-Making, Economics and Finance, 249-269. Kluwer.
- Schweizer, M. (2010). Mean-Variance Hedging. Encyclopedia of Quantitative Finance. Wiley.
- Shoesmith, E. (1986). Huygens’ Solution to the Gambler’s Ruin Problem. Historia Mathematica, 13(2), 157-164.
- Song, S., & Song, J. (2013). A Note on the History of the Gambler’s Ruin Problem. Communications for Statistical Applications and Methods, 20(2), 157-168.
- Thomson, R. (2005). The Pricing of Liabilities in an Incomplete Market using Dynamic Mean-Variance Hedging. Insurance: Mathematics and Economics 36, 441-455.
- Vila, J., & Zariphopoulou, T. (1997). Optimal Consumption and Portfolio Choice with Borrowing Constraints. Journal of Economic Theory, 77, 402-431.
- Wolf, M. (2008). Why Today’s Hedge Fund Industry May not Survive. Financial Times, 18(March).
