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Signature Methods for Optimal Market Making

  • Alberto Gennaro
  • Thibaut Mastrolia
  • Francesca Primavera
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Abstract

We propose a signature-based method to solve the optimal market-making problem under a mean-variance criterion. By exploiting signature linearization techniques, we reduce the market-making problem to a pseudo-linear optimization over the expected signature of an augmented market path, and we develop a signature algorithm named Sig-REINFORCE to learn the optimal bid and ask quotes. We test our method in two scenarios, in which market-order arrivals follow either a Poisson or a self-exciting Hawkes process, and we benchmark it against a Proximal Policy Optimization (PPO) baseline.

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Cite

BibTeXRIS
BibTeX
@misc{gennaro2026signature,
  title = {{Signature Methods for Optimal Market Making}},
  author = {Alberto Gennaro and Thibaut Mastrolia and Francesca Primavera},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.19772},
  eprint = {2606.19772},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19772},
}
RIS
TY  - UNPB
TI  - Signature Methods for Optimal Market Making
AU  - Alberto Gennaro
AU  - Thibaut Mastrolia
AU  - Francesca Primavera
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2606.19772
UR  - https://arxiv.org/abs/2606.19772
AB  - We propose a signature-based method to solve the optimal market-making problem under a mean-variance criterion. By exploiting signature linearization techniques, we reduce the market-making problem to a pseudo-linear optimization over the expected signature of an augmented market path, and we develop a signature algorithm named Sig-REINFORCE to learn the optimal bid and ask quotes. We test our method in two scenarios, in which market-order arrivals follow either a Poisson or a self-exciting Hawkes process, and we benchmark it against a Proximal Policy Optimization (PPO) baseline.
ER  -