Liquidity Provision with Adverse Selection and Inventory Costs

Martin Herdegen (), Johannes Muhle-Karbe () and Florian Stebegg ()
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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

Mathematics of Operations Research, 2023, vol. 48, issue 3, 1286-1315

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.

Keywords: Primary: 91A15; 91B26; 91B54; secondary: 49J55; liquidity provision; Nash competition; adverse selection; inventory cost (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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