Derives local affine structure for Brownian signature transforms via infinite-dimensional linear and Riccati equations on the extended tensor algebra, with randomized versions for global representations.
Signature Methods for Optimal Market Making
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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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2026 1verdicts
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Fourier-Laplace Transforms of the Brownian Signature via Riccati Equations on the Tensor Algebra
Derives local affine structure for Brownian signature transforms via infinite-dimensional linear and Riccati equations on the extended tensor algebra, with randomized versions for global representations.