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Main Authors: Boyce, Robert, Herdegen, Martin, Sánchez-Betancourt, Leandro
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.17393
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author Boyce, Robert
Herdegen, Martin
Sánchez-Betancourt, Leandro
author_facet Boyce, Robert
Herdegen, Martin
Sánchez-Betancourt, Leandro
contents We study liquidity provision in the presence of exogenous competition. We consider a `reference market maker' who monitors her inventory and the aggregated inventory of the competing market makers. We assume that the competing market makers use a `rule of thumb' to determine their posted depths, depending linearly on their inventory. By contrast, the reference market maker optimises over her posted depths, and we assume that her fill probability depends on the difference between her posted depths and the competition's depths in an exponential way. For a linear-quadratic goal functional, we show that this model admits an approximate closed-form solution. We illustrate the features of our model and compare against alternative ways of solving the problem either via an Euler scheme or state-of-the-art reinforcement learning techniques.
format Preprint
id arxiv_https___arxiv_org_abs_2407_17393
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Market Making with Exogenous Competition
Boyce, Robert
Herdegen, Martin
Sánchez-Betancourt, Leandro
Mathematical Finance
93E20, 91B70, 49L20
We study liquidity provision in the presence of exogenous competition. We consider a `reference market maker' who monitors her inventory and the aggregated inventory of the competing market makers. We assume that the competing market makers use a `rule of thumb' to determine their posted depths, depending linearly on their inventory. By contrast, the reference market maker optimises over her posted depths, and we assume that her fill probability depends on the difference between her posted depths and the competition's depths in an exponential way. For a linear-quadratic goal functional, we show that this model admits an approximate closed-form solution. We illustrate the features of our model and compare against alternative ways of solving the problem either via an Euler scheme or state-of-the-art reinforcement learning techniques.
title Market Making with Exogenous Competition
topic Mathematical Finance
93E20, 91B70, 49L20
url https://arxiv.org/abs/2407.17393