Paper: arXiv 2312.16448

Abstract

We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously ill defined due to small signal to noise ratio, one can still try to learn optimal non-linear maps from data to future returns for the purposes of portfolio optimization. Randomized Signatures, in contrast to classical signatures, allow for high dimensional market dimension and provide features on the same scale. We do not contribute to the theory of Randomized Signatures here, but rather present our empirical findings on portfolio selection in real world settings including real market data and transaction costs.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts from rough path theory and randomized signatures, involving non-linear drift estimation and high-dimensional feature mapping. It is evaluated on real market data with transaction costs and compares against standard benchmarks, indicating strong empirical validation and implementation focus.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Apply Randomized Signatures<br/>to Optimal Portfolio Selection"] --> B["Data Inputs<br/>Real Market Data: Equities<br/>Including Transaction Costs"]
  B --> C["Methodology:<br/>Randomized Signature Methods"]
  C --> D["Computational Process:<br/>Non-linear, Non-parametric<br/>Drift Estimation"]
  D --> E["Outcome:<br/>Learn Optimal Maps<br/>for Future Returns"]
  E --> F["Key Finding:<br/>Effective Portfolio Selection<br/>in Real-World Settings"]

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1 of 89 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.