Drawdown and Drawup of Bi-Directional Grid Constrained Stochastic Processes

Taranto, Aldo ORCID: https://orcid.org/0000-0001-6763-4997 and Khan, Shahjahan (2020) Drawdown and Drawup of Bi-Directional Grid Constrained Stochastic Processes. Journal of Mathematics and Statistics, 16 (1). pp. 182-197. ISSN 1549-3644

[img]
Preview
Text (Published Version)
jmssp.2020.182.197.pdf
Available under License Creative Commons Attribution.

Download (1MB) | Preview

Abstract

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 E_t 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.


Statistics for USQ ePrint 39564
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sept 2019 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sept 2019 -)
Date Deposited: 15 Sep 2020 00:30
Last Modified: 30 Sep 2020 03:04
Uncontrolled Keywords: 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)
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0102 Applied Mathematics > 010205 Financial Mathematics
01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970108 Expanding Knowledge in the Information and Computing Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970114 Expanding Knowledge in Economics
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.3844/jmssp.2020.182.197
URI: http://eprints.usq.edu.au/id/eprint/39564

Actions (login required)

View Item Archive Repository Staff Only