Finding moving-band statistical arbitrages via convex–concave optimization

We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex,...

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Bibliographic Details
Published in:Optimization and engineering Vol. 26; no. 2; pp. 1203 - 1224
Main Authors: Johansson, Kasper, Schmelzer, Thomas, Boyd, Stephen
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.06.2025
Subjects:
Asset acquisitions
Convexity
Machine learning
Optimization
Prices
Profits
Stochastic control theory
Time series
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary:We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex, but can be approximately solved using the convex–concave procedure, a specific sequential convex programming method. We show how the method generalizes to finding moving-band statistical arbitrages, where the price band midpoint varies over time.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-024-09933-0