Stochastic factors can matter: improving robust growth under ergodicity

Paper: arXiv 2512.24906

Authors: Balint Binkert, David Itkin, Paul Mangers Bastian, Josef Teichmann

Abstract

Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization in a high-dimensional incomplete market under drift uncertainty of the asset price process $X$, under an additional ergodicity assumption, which constrains but does not fully specify the drift in general. The class of admissible models allows $X$ to depend on a multivariate stochastic factor $Y$ and fixes (a) their joint volatility structure, (b) their long-term joint ergodic density and (c) the dynamics of the stochastic factor process $Y$. A principal motivation of this framework comes from pairs trading, where $X$ is the spread process and models with the above characteristics are commonplace. Our main results determine the robust optimal growth rate, construct a worst-case admissible model and characterize the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE). We demonstrate that utilizing the stochastic factor leads to improvement in robust growth complementing the conclusions of the previous study by Itkin et. al. (arXiv:2211.15628 [q-fin.MF], forthcoming in $\textit{Finance and Stochastics}$), which additionally robustified the dynamics of the stochastic factor leading to $Y$-independent optimal strategies. Our analysis leads to new financial insights, quantifying the improvement in growth the investor can achieve by optimally incorporating stochastic factors into their trading decisions. We illustrate our theoretical results on several numerical examples including an application to pairs trading.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic analysis, PDEs, and calculus of variations to solve a robust growth-optimization problem in high dimensions. While it includes numerical illustrations and applications to pairs trading, it lacks extensive empirical backtesting on real-world market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve robust portfolio growth under drift uncertainty using stochastic factors] --> B[Inputs: Asset process X, factor Y, volatility, ergodic density & Y-dynamics]
    B --> C[Methodology: Formulate robust growth-optimization model for incomplete markets]
    C --> D[Computational Process: Solve non-linear PDE for robust optimal strategy & worst-case model]
    D --> E[Application: Numerical examples & Pairs Trading implementation]
    E --> F[Outcomes: Quantified growth improvement by incorporating Y; optimal factor-dependent strategy]

Cited References (251)

1. On the performance of delta hedging strategies in exponential L 'e vy models (2013)
2. Algorithmic and High-Frequency Trading (2015)
3. Adaptive execution: Exploration and learning of price impact (2015)
4. Statistical Learning with Sublinear Regret of Propagator Models — → 2301.05157
5. Dynamic Replication and Hedging: A Reinforcement Learning Approach (2019)
6. On parametric optimal execution and machine learning surrogates (2024)
7. An optimal control strategy for execution of large stock orders using long short-term memory networks (2023)
8. Adam: A Method for Stochastic Optimization (2015)

6 of 251 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.