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Optimal Investment and Consumption for OU Pairs Trading

Article arXiv papers · Author: Sahar Albosaily et al.
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Summary

This paper studies an investment and consumption problem in a pairs trading market where the spread between risky assets follows an Ornstein–Uhlenbeck process. It focuses on optimal strategies under power utility, bringing together portfolio decisions and consumption choices in a mean-reverting market setting.

The authors use the Feynman–Kac method to study the associated Hamilton–Jacobi–Bellman equation and report existence and uniqueness of a classical solution. They also examine a numerical approximation and establish a convergence rate, described in the abstract as extremely explosive. The provided text does not give the model’s full assumptions, parameter choices, approximation details, or practical trading results. It therefore offers a mathematical framework and reported solution properties, but not enough information to assess implementation costs, robustness, or real-world performance.

Key ideas

  • The risky-asset spread is modeled as an Ornstein–Uhlenbeck process.
  • The investment and consumption objective uses power utility.
  • The Feynman–Kac method is applied to study the Hamilton–Jacobi–Bellman equation.
  • The paper reports existence and uniqueness of a classical solution.
  • A numerical approximation is studied, with its convergence rate described as extremely explosive.

Tags

Pairs tradingMean reversionStatisticsPortfolio construction
Full text
# Optimal investment and consumption for pairs trading financial markets on small time interval


# Optimal investment and consumption for pairs trading financial markets on small time interval









In this paper we consider a pairs trading financial market with the spread of risky assets defined by the Ornstein-Uhlenbeck (OU) process. We implement an optimal strategy for power utility functions for investment/consumption problem. Through the Feynman-Kac (FK) method, we study the Hamilton-Jacobi-Bellman (HJB) equation for this problem. Moreover, the existence and uniqueness has been shown for classical solution for the HJB equation. In addition, the numeric approximation for the solution of the HJB equation has been studied and the convergence rate has been established and it is been found that the convergence rate is extremely explosive.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.