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Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process

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  • Arne Lokka
  • Junwei Xu

Abstract

In a one-sided limit order book, satisfying some realistic assumptions, where the unaffected price process follows a Levy process, we consider a market agent that wants to liquidate a large position of shares. We assume that the agent has constant absolute risk aversion and aims at maximising the expected utility of the cash position at the end of time. The agent is then faced with the problem of balancing the market risk and the cost of a rapid execution. In particular we are interested in how the agent should go about optimally submitting orders. Since liquidation normally takes place within a short period of time, modelling the risk as a Levy process should provide a realistic model with good statistical fit to observed market data, and thus the model should provide a realistic reflection of the agent's market risk. We reduce the optimisation problem to a deterministic two-dimensional singular problem, to which we are able to derive an explicit solution in terms of the model data. In particular we find an expression for the optimal intervention boundary, which completely characterise the optimal liquidation strategy.

Suggested Citation

  • Arne Lokka & Junwei Xu, 2020. "Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process," Papers 2002.03379, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:2002.03379
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    References listed on IDEAS

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    Cited by:

    1. Ulrich Horst & Evgueni Kivman, 2021. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Papers 2103.05957, arXiv.org, revised Jul 2023.
    2. Ulrich Horst & Evgueni Kivman, 2024. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Finance and Stochastics, Springer, vol. 28(3), pages 759-812, July.

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