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Liquidity Provision with Adverse Selection and Inventory Costs

Author

Listed:
  • Martin Herdegen

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom)

  • Johannes Muhle-Karbe

    (Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom)

  • Florian Stebegg

    (Department of Statistics, Columbia University, New York, New York 10027)

Abstract

We study one-shot Nash competition between an arbitrary number of identical dealers that compete for the order flow of a client. The client trades either because of proprietary information, exposure to idiosyncratic risk, or a mix of both trading motives. When quoting their price schedules, the dealers do not know the client’s type but only its distribution, and in turn choose their price quotes to mitigate between adverse selection and inventory costs. Under essentially minimal conditions, we show that a unique symmetric Nash equilibrium exists and can be characterized by the solution of a nonlinear ordinary differential equation.

Suggested Citation

  • Martin Herdegen & Johannes Muhle-Karbe & Florian Stebegg, 2023. "Liquidity Provision with Adverse Selection and Inventory Costs," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1286-1315, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1286-1315
    DOI: 10.1287/moor.2022.1294
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