TY  - JOUR
AU  - Taranto, Aldo 
AU  - Khan, Shahjahan 
PY  - 2020
TI  - Drawdown and Drawup of Bi-Directional Grid Constrained Stochastic Processes
JF  - Journal of Mathematics and Statistics
VL  - 16
IS  - 1
DO  - 10.3844/jmssp.2020.182.197
UR  - https://thescipub.com/abstract/jmssp.2020.182.197
AB  - 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.