Drawdown and Drawup of Bi-Directional Grid Constrained Stochastic Processes
- 1 University of Southern Queensland, Australia
Copyright: © 2020 Aldo Taranto and Shahjahan Khan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The Grid Trading Problem (GTP) of mathematical finance, used in portfolio loss minimization, generalized dynamic hedging and algorithmic trading, is researched by examining the impact of the drawdown and drawup of discrete random walks and of Itô diffusions on the Bi-Directional Grid Constrained (BGC) stochastic process for profit Pt and equity Et over time. A comprehensive Discrete Difference Equation (DDE) and a continuous Stochastic Differential Equation (SDE) are derived and proved for the GTP. This allows fund managers and traders the ability to better stress test the impact of volatility to reduce risk and generate positive returns. These theorems are then simulated to complement the theoretical models with charts. Not only does this research extend a rich mathematical problem that can be further researched in its own right, but it also extends the applications into the above areas of finance.
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- Grid Trading Problem (GTP)
- Bi-Directional Grid Constrained (BGC)
- Random Walks
- Itô Diffusions
- Probability of Ruin
- Maximal Drawdown
- Maximal Drawup
- Discrete Difference Equation (DDE)
- Stochastic Differential Equation (SDE)