Liquidity Provision with Adverse Selection and Inventory Costs

35 Pages Posted: 28 Jul 2021

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Florian Stebegg

Columbia University - Departments of Statistics and Mathematics

Date Written: July 26, 2021

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 ODE.

Keywords: liquidity provision, Nash competition, adverse selection, inventory costs

JEL Classification: C61, C72, C78, G14

Suggested Citation

Herdegen, Martin and Muhle-Karbe, Johannes and Stebegg, Florian, Liquidity Provision with Adverse Selection and Inventory Costs (July 26, 2021). Available at SSRN: https://ssrn.com/abstract=3893519 or http://dx.doi.org/10.2139/ssrn.3893519

Martin Herdegen

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Florian Stebegg

Columbia University - Departments of Statistics and Mathematics ( email )

1255 Amsterdam Avenue
New York, NY 10027
United States

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