Stochastic portfolio theory with price impact

[2506.07993] Stochastic portfolio theory with price impact Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantitative Finance > Mathematical Finance arXiv:2506.07993 (q-fin) [Submitted on 9 Jun 2025 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Stochastic portfolio theory with price impact Authors: David Itkin View a PDF of the paper titled Stochastic portfolio theory with price impact, by David Itkin View PDF HTML (experimental) Abstract: We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of trading strategies in a general high-dimensional market model with price impact. We also derive formulas for an investor's relative wealth with respect to the market portfolio, conditions that guarantee positive observed market prices and a stochastic differential equation governing the dynamics of the observed price, the investor's holdings and the price impact state processes. As an application of these results, we develop conditions for relative arbitrage in the price impact setting analogous to previously obtained results for the frictionless setting. We then apply our framework to backtest the quadratic and entropy generating functions on historical US equity data, illustrating how price impact can negatively affect portfolio performance. Comments: Results expanded to include empirical experiments, discuss multiplicative generation and discuss connections between additive generation and CARA utility. Lemma 5.8 and Theorem 5.9 also updated and the presentation of the results streamlined Subjects: Mathematical Finance (q-fin.MF) ; Probability (math.PR) MSC classes: 91G10, 60H30 Cite as: arXiv:2506.07993 [q-fin.MF] (or arXiv:2506.07993v3 [q-fin.MF] for this version) https://doi.org/10.48550/arXiv.2506.07993 Focus to learn more arXiv-issued DOI via DataCite Submission history From: David Itkin [ view email ] [v1] Mon, 9 Jun 2025 17:57:46 UTC (182 KB) [v2] Wed, 18 Jun 2025 17:08:03 UTC (182 KB) [v3] Tue, 14 Apr 2026 11:23:47 UTC (3,244 KB) Full-text links: Access Paper: View a PDF of the paper titled Stochastic portfolio theory with price impact, by David Itkin View PDF HTML (experimental) TeX Source view license Current browse context: q-fin.MF < prev | next > new | recent | 2025-06 Change to browse by: math math.PR q-fin References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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