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Some Computations for Optimal Execution with Monotone Strategies

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  • Yan Dolinsky

Abstract

We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the number of shares and the selling rate are non-negative processes. For this case we give a complete characterization of the value and the optimal control via a solution of a non-linear ordinary differential equation (ODE). Furthermore, we provide an example where the non-linear ODE can be solved explicitly. Our approach is purely probabilistic.

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  • Yan Dolinsky, 2024. "Some Computations for Optimal Execution with Monotone Strategies," Papers 2411.10726, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2411.10726
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    References listed on IDEAS

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    1. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
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