Seminar with Bartosz Bieganowski – April 27

On April 27 at 18:30, a seminar jointly organized by the Quantitative Finance Research Group (QFRG WNE UW) and DSLab WNE UW will be held. This session features Bartosz Bieganowski, affiliated with the Department of Quantitative Finance and Machine Learning, who will present research conducted alongside Prof. Robert Ślepaczuk. The study is titled Optimal Market Making under Exchange Rate Limits. We invite you to read the abstract provided below.

The meeting will be held in a hybrid format- on-site at the Faculty of Economic Sciences, University of Warsaw (Długa 44/50, Warsaw) in Room B002, and remotely via Zoom. The presentation is scheduled for 45 minutes, followed by an open discussion. We kindly ask participants to arrive or log in a few minutes early.

The meeting link will be provided upon request. Please email: LosIxpnbM#Vg8X_lE'-Y=e]#[9bc3hTYDd}EMENWu%g}b#R

Abstract:

Market makers on modern electronic exchanges face a fundamental tension: frequent requoting improves quote positioning but consumes finite rate-limit tokens imposed by the exchange. We model this as a hybrid impulse-control problem within the Avellaneda-Stoikov framework, where the agent optimizes CARA utility subject to a token-bucket constraint on order placements and cancellations. Treating the inaction bandwidth (the maximum tolerable quote drift before repricing) as the central decision variable, we derive a closed-form approximation for the optimal threshold under Poisson fill arrivals: the optimal bandwidth scales as the fourth root of the ratio of volatility to inventory risk and rate-limit cost, yielding a Fourth-Root Law that makes the trade-off between quote staleness and token consumption explicit. We then train a Proximal Policy Optimization (PPO) agent with a structurally symmetric two-phase architecture, enforcing exact bid/ask symmetry by construction rather than by learning, and a continuous tolerance action that maps directly to the theoretical inaction bandwidth. The learned value function serves as a reward forecast, identifying the repricing threshold as the point where expected repositioning gains exceed rate-limit opportunity costs. Sensitivity analysis across a grid of volatility and fill-rate parameters confirms that the agent recovers the qualitative predictions of the closed-form solution: wider spreads and larger inaction bandwidths under high volatility, tighter spreads and more aggressive repricing when fill rates are high. For the multi-asset case with a shared rate-limit pool, we derive an optimal allocation rule where the fraction of tokens devoted to an asset is proportional to the product of its volatility and square root of its fill sensitivity. We then verify that the PPO agent trained on a two-asset environment with heterogeneous parameters converges to this proportional allocation. These results bridge analytical market-making theory, deep reinforcement learning, and technological reality of being a market maker on modern electronic exchanges by offering both interpretable closed-form guidance and an empirically validated RL framework for rate-constrained liquidity provision.

Keywords: large language models, LASSO, SVR, HAR, machine learning, cryptocurrencies, Bitcoin returns, volatility