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

TL;DR

This paper develops an optimal investment and consumption strategy in a pairs trading market modeled by an Ornstein-Uhlenbeck process, using HJB equations and numerical methods to analyze solution properties and convergence.

Contribution

It introduces a novel approach to optimal trading strategies in pairs markets with OU spread dynamics, including existence, uniqueness, and numerical convergence analysis.

Findings

Existence and uniqueness of classical solution to HJB equation established.

Numerical approximation methods with proven convergence rate.

Explosive convergence rate observed in numerical solutions.

Abstract

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.