Mathematical Modeling
Vol. 8 (2024), Issue 2, pg(s) 75-80

MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

Classical Optimization methods for an Ornstein-Uhlenbeck process-based model in pair trading

  • 1 Faculty of Computer Science and Engineering University of Ss. Cyril and Methodius Skopje, North Macedonia

Abstract

Mathematical Optimization or Mathematical Programming is a set of theoretical and applied methods originating from applied mathematics to computer science, used to find the optimal value, given some predefined criterion for optimality and based on some input parameters. More precisely, it concerns finding the input parameters of a function (called the objective function) which maximize/minimize its output. Mathematical Optimization is widely used for various quantitative or computational problems that arise everywhere in science and engineering, ranging from statistics and applied math to aerospace engineering and finance. In the following paper, we demonstrate the use of two classical optimization algorithms – Gradient Descent and Lagrangian Multipliers method – in model development in finance and trading. The specific stochastic process on which the trading model is based is called the Ornstein-Uhlenbeck (O-U) process and the point of the use of these two optimization approaches is
to find the parameters that minimize the log likelihood function of this process. This fits the O-U process to the historical data and in the context of finance and trading, maximizes our profits and helps us hedge against losses

Keywords

References

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