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Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals

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  • Fayçal Drissi

Abstract

We study a differential Riccati equation (DRE) with indefinite matrix coefficients, which arises in a wide class of practical problems. We show that the DRE solves an associated control problem, which is key to provide existence and uniqueness of a solution. As an application, we solve two algorithmic trading problems in which the agent adopts a constant absolute risk-aversion (CARA) utility function, and where the optimal strategies use signals and past observations of prices to improve their performance. First, we derive a multi-asset market making strategy in over-the-counter markets, where the market maker uses an external trading venue to hedge risk. Second, we derive an optimal trading strategy that uses prices and signals to learn the drift in the asset prices.

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  • Fayçal Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(6), pages 457-493, November.
    • Handle: RePEc:taf:apmtfi:v:29:y:2022:i:6:p:457-493
    DOI: 10.1080/1350486X.2023.2241130
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    Cited by:

    1. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    2. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Papers 2405.03496, arXiv.org, revised May 2024.
    3. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    4. Alvaro Arroyo & Alvaro Cartea & Fernando Moreno-Pino & Stefan Zohren, 2023. "Deep Attentive Survival Analysis in Limit Order Books: Estimating Fill Probabilities with Convolutional-Transformers," Papers 2306.05479, arXiv.org.
    5. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.

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