# Signature Methods in Stochastic Portfolio Theory

arXiv: https://arxiv.org/abs/2310.02322 · HTML: https://mlsanity.com/paper/2310.02322/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2023.

## Built on by (most cited first, 11 of 11)

- [pySigLib -- Fast Signature-Based Computations on CPU and GPU](https://mlsanity.com/paper/2509.10613/) (2025)
- [Randomized Signature Methods in Optimal Portfolio Selection](https://mlsanity.com/paper/2312.16448/) (2023)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Universal approximation with signatures of non-geometric rough paths](https://mlsanity.com/paper/2602.05898/) (2026)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Kernel Learning for Mean-Variance Trading Strategies](https://mlsanity.com/paper/2507.10701/) (2025)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)

## Abstract (arXiv)

In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals of an underlying semimartingale. As main example for such feature maps we consider the signature of the (ranked) market weights. We prove that these portfolios are universal in the sense that every continuous, possibly path-dependent, portfolio function of the market weights can be uniformly approximated by signature portfolios. We also show that signature portfolios can approximate the growth-optimal portfolio in several classes of non-Markovian market models arbitrarily well and illustrate numerically that the trained signature portfolios are remarkably close to the theoretical growth-optimal portfolios. Besides these universality features, the main numerical advantage lies in the fact that several optimization tasks like maximizing (expected) logarithmic wealth or mean-variance optimization within the class of linear path-functional portfolios reduce to a convex quadratic optimization problem, thus making it computationally highly tractable. We apply our method also to real market data based on several indices. Our results point towards out-performance on the considered out-of-sample data, also in the presence of transaction costs.