Optimal pair trading: consumption-investment problem

Paper: arXiv 2312.06842

Authors: Yuri Kabanov, Aleksei Kozhevnikov

Abstract

We expose a simple solution of the consumption-investment problem pair trading. The proof is based on the remark that the HJB equation can be reduced to a linear parabolic equation solvable explicitly.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical contribution by showing that the Hamilton-Jacobi-Bellman (HJB) equation for a pair trading portfolio problem reduces to an explicitly solvable linear parabolic equation. However, it is largely theoretical and lacks empirical validation or backtesting on real market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Pair Trading<br/>Consumption-Investment Problem] --> B[Inputs: Equities Data & Asset Prices]
    B --> C[Formulate Stochastic Control Problem<br/>via HJB Equation]
    C --> D[Reduce HJB Equation to<br/>Linear Parabolic Equation]
    D --> E[Derive Explicit Analytical Solution]
    E --> F[Outcome: Optimal Trading Strategy &<br/>Simplified Consumption-Investment Model]