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

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  • Fayc{c}al 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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  • Fayc{c}al Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Papers 2202.07478, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2202.07478
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    References listed on IDEAS

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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. '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 Apr 2024.
    3. Dammann, Felix & Ferrari, Giorgio, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Center for Mathematical Economics Working Papers 663, Center for Mathematical Economics, Bielefeld University.
    4. Felix Dammann & Giorgio Ferrari, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Papers 2202.10414, arXiv.org, revised Nov 2022.
    5. 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.

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