Paper: arXiv 2506.19715

Authors: Michael Monoyios, Olivia Pricilia

Abstract

We introduce a novel neural-network-based approach to learning the generating function $G(\cdot)$ of a functionally generated portfolio (FGP) from synthetic or real market data. In the neural network setting, the generating function is represented as $G_θ(\cdot)$, where $θ$ is an iterable neural network parameter vector, and $G_θ(\cdot)$ is trained to maximise investment return relative to the market portfolio. We compare the performance of the Neural FGP approach against classical FGP benchmarks. FGPs provide a robust alternative to classical portfolio optimisation by bypassing the need to estimate drifts or covariances. The neural FGP framework extends this by introducing flexibility in the design of the generating function, enabling it to learn from market dynamics while preserving self-financing and pathwise decomposition properties.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is heavily mathematical, featuring advanced stochastic calculus, partial differential equations, and pathwise decomposition theorems typical of Stochastic Portfolio Theory. However, it lacks specific backtesting results, performance metrics, or implementation details, relying instead on synthetic data and theoretical propositions rather than real-world empirical validation.

Research Flowchart

  flowchart TD
  A["Research Goal: Learn generating function G_θ(·)<br>to optimize portfolio return"] --> B["Neural FGP Methodology"]
  
  B --> C["Data Input: Synthetic/Real Market Data"]
  
  C --> D["Computational Process: Train G_θ(·)<br>via Maximizing Investment Return"]
  
  D --> E["Preserve Self-Financing &<br>Pathwise Decomposition Properties"]
  
  E --> F["Compare against Classical FGP Benchmarks"]
  
  F --> G["Key Findings: Neural FGP outperforms benchmarks<br>with flexible learning from market dynamics<br>while maintaining robustness without<br>drift/covariance estimation"]

Cited References (15)

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  8. Stochastic Portfolio Theory (2002) — link
and 7 more
  1. On the diversity of equity markets (1999) — link
  2. Portfolio Generating Functions (1998) — link
  3. A general version of the fundamental theorem of asset pricing (1994) — link
  4. ON THE REPRESENTATION OF SEMIMARTINGALES (1973) — link
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  7. Stochastic Portfolio Theory: an Overview (2009) — link

0 of 15 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.