Stochastic Control Models for Ornstein–Uhlenbeck Pairs Trading
Summary
This introduction reviews stochastic control models for allocating wealth between a mean-reverting spread and a risk-free asset. It describes the spread with an Ornstein–Uhlenbeck process and outlines work by Jurek and Yang, which considers investors with constant relative risk aversion and recursive Epstein–Zin preferences over a finite horizon. The analysis uses the asset dynamics to formulate wealth and budget equations, then applies a Hamilton–Jacobi–Bellman equation to derive value and investment policy functions.
The document also notes work by Mudchanatongsuk and coauthors, who solve a pairs-trading control problem under power utility for terminal wealth, using a different asset-pricing setup that still includes an OU spread. This is a brief literature overview, not a full derivation or trading recipe. It reports no empirical performance, and its conclusions depend on the assumed spread dynamics, investor preferences, and model setup.
Key ideas
- An Ornstein–Uhlenbeck process represents the mean-reverting spread in the reviewed models.
- Stochastic control frames the allocation between a spread position and a risk-free asset as a wealth optimization problem.
- Jurek and Yang derive value and policy functions for two investor preference specifications.
- A separate model studies terminal-wealth optimization under power utility with OU-based spread dynamics.
- The overview provides no empirical trading results.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.