arXiv subjects

Leandro Sánchez-Betancourt

Publications and source records attributed to Leandro Sánchez-Betancourt.

At least 19 recordsLinked to original sources

arXiv2026

When Hedging Changes the Payoff: Option Replication with Price Impact and Execution Costs

Hedging a derivative by trading the underlying asset changes the payoff that the hedging intended to replicate. We study this phenomenon when trading generates price impact and execution costs. In a binomial model, we characterize replication through a fixed-point equation. In continuous time, we derive a nonlinear pricing PDE whose implicit terminal condition captures the nature of the moving target problem of the hedger. For monotone convex Lipschitz payoffs (such as calls and puts) we establish exact replication under midpoint execution costs. Numerical experiments illustrate: (i) how price impact shifts the effective strike, (ii) the non-linear dependence of the option price on the number of contracts, (iii) how execution costs smooth terminal holdings, (iv) the extent to which the hedger's own trading can bring an otherwise worthless option into the money, and (v) we explain the spread and the shape of the limit order book in the options market based on the price impact and the shape of the limit order book of the underlying.

q-fin.MF↗

arXiv2026

SAiFE-gym: Model-based Environments for Automated Market Making with Concentrated Liquidity

We present SAiFE_gym, a Python module that provides a collection of simulation environments for studying trading problems in Constant Product Markets (CPMs) with Concentrated Liquidity (CL). These markets give Liquidity Providers (LPs) granular control over how their capital is allocated and enable them to adjust their range of liquidity provision dynamically based on market conditions, which in turn, dictates how they earn fees. We decompose the microstructure of CPMs with CL in interactive components that allow researchers and practitioners to capture various economic settings. We employ a vectorized approach to optimize our environments, making them scalable for high dimensional Reinforcement Learning (RL) workflows that best describe sequential decision problems. We demonstrate the benefits of our environments by evaluating the performance of RL agents in CPMs with CL under uncertainty in market parameters.

q-fin.TR↗

arXiv2026

Concentrated Liquidity Provision: a Reinforcement Learning Perspective

Automated market makers (AMMs) are a cornerstone of decentralised finance (DeFi). Constant product markets with concentrated liquidity, such as UniswapV3, are now a well-established design. In these markets, liquidity providers (LPs) face a sequential decision problem: they must decide when to rebalance their positions and which price ranges to allocate capital to as market conditions evolve. We formulate dynamic liquidity provision as a stochastic impulse control problem and use reinforcement learning (RL) to solve it, focusing on providing interpretable solutions. We show that learned policies exhibit rich state-dependent behaviour, allocating liquidity according to mispricing, rebalancing costs, uncertainty, inventory exposure, and heterogeneous risk preferences. These behaviours help compress the left tail of the Profit and Loss (PnL) distribution and avoid catastrophic outcomes under high uncertainty. Finally, we benchmark the RL agents against baseline and sophisticated agents from the AMM microstructure literature and analyse their performance.

q-fin.TR↗

arXiv2026

Optimal Dynamic Fees in Automated Market Makers

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.

q-fin.TR↗

arXiv2026

Market Making with Fads, Informed, and Uninformed Traders

We characterise the solution to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads -- these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad, we model how informed traders and uninformed traders arrive in the market. The market maker is aware of the existence of the two groups of traders but only observes the anonymous order arrivals. We study both, the complete and the partial information versions of the control problem faced by the market maker. In such frameworks, we characterise the value of information, and we find the price of liquidity as a function of the proportion of informed traders in the market. We discuss how to calibrate model parameters from market data and we quantify the outperformance over strategies that ignore these unobservable short-term deviations.} Lastly, for the partial information setup, we explore how to go beyond the Kalman-Bucy filter to extract information about the fad from the market arrivals.

q-fin.TR↗

arXiv2026

Doubly Outlier-Robust Online Infinite Hidden Markov Model

We derive a robust update rule for the online infinite hidden Markov model (iHMM) for when the streaming data contains outliers and the model is misspecified. Leveraging recent advances in generalised Bayesian inference, we define robustness via the posterior influence function (PIF), and provide conditions under which the online iHMM has bounded PIF. Imposing robustness inevitably induces an adaptation lag for regime switching. Our method, which is called Batched Robust iHMM (BR-iHMM), balances adaptivity and robustness with two additional tunable parameters. Across limit order book data, hourly electricity demand, and a synthetic high-dimensional linear system, BR-iHMM reduces one-step-ahead forecasting error by up to 67% relative to competing online Bayesian methods. Together with theoretical guarantees of bounded PIF, our results highlight the practicality of our approach for both forecasting and interpretable online learning.

stat.ML↗

arXiv2026

Solving Linear-Quadratic Stochastic Control Problems with Signatures

We study a signature-driven numerical scheme to solve multi-dimensional linear-quadratic (LQ) stochastic control problems. Using that linear signature functionals are dense in the natural class of admissible controls, we show that our approach turns the original LQ problem into a deterministic convex quadratic polynomial optimisation. To underpin a numerical approach based on truncated signatures, we prove that the problem's value function can be approximated by finite-dimensional polynomial approximations when the truncation levels are chosen sufficiently high. Remarkably, our numerical experiments show very decent accuracy already for small truncation levels. Key tools for our analysis are (i) the algebraic representation of controlled stochastic differential equations and the associated cost function as linear functionals of the path signatures of the driving noise, (ii) the convergence of the truncated linear functionals, and (iii) the density of signature controls.

math.OC↗

arXiv2026

Trading in CEXs and DEXs with Priority Fees and Stochastic Delays

We develop a mixed control framework that combines absolutely continuous controls with impulse interventions subject to stochastic execution delays. The model extends current impulse control formulations by allowing (i) the controller to choose the mean of the stochastic delay of their impulses, and allowing (ii) for multiple pending orders, so that several impulses can be submitted and executed asynchronously at random times. The framework is motivated by an optimal trading problem between centralized (CEX) and decentralized (DEX) exchanges. In DEXs, traders control the distribution of the execution delay through the priority fee paid, introducing a fundamental trade-off between delays, uncertainty, and costs. We study the optimal trading problem of an agent exploiting trading signals in CEXs and DEXs. From a mathematical perspective, we derive the associated dynamic programming principle of this new class of impulse control problems, and establish the viscosity properties of the corresponding quasi-variational inequalities. From a financial perspective, our model provides insights on how to carry out execution across CEXs and DEXs, highlighting how traders manage latency risk optimally through priority fee selection. We show that employing the optimal priority fee has a significant outperformance over non-strategic fee selection.

q-fin.TR↗

arXiv2026

Strategic Learning and Trading in Broker-Mediated Markets

We study strategic interactions in a broker-mediated market in which agents learn and exploit each other's private information. A broker provides liquidity to an informed trader and to noise traders while managing inventory in a lit market. The informed trader infers the broker's trading activity in the lit market, while the broker estimates the trader's private signal. Information leakage in the client's trading flow generates economic value for the broker that is comparable in magnitude to transaction costs: the broker can speculate profitably and manage risk more effectively, which in turn adversely affects the informed trader's performance. Brokers therefore hold a strategic advantage over traders who rely solely on prices to filter information. When the broker only relies on prices rather than client trading flow to infer information, their trading performance becomes indistinguishable from the performance of a naive strategy that internalises noise flow, externalises informed flow, and offloads inventory at a constant rate.

q-fin.TR↗

arXiv2026

Detecting Toxic Flow

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-efficient Bayesian procedure for online training of neural networks. We employ a proprietary dataset of foreign exchange transactions to test our methodology. Neural networks trained with PULSE outperform standard machine learning and statistical methods when predicting if a trade will be toxic; the benchmark methods are logistic regression, random forests, and a recursively-updated maximum-likelihood estimator. We devise a strategy for the broker who uses toxicity predictions to internalise or to externalise each trade received from her clients. Our methodology can be implemented in real-time because it takes less than one millisecond to update parameters and make a prediction. Compared with the benchmarks, online learning of a neural network with PULSE attains the highest PnL and avoids the most losses by externalising toxic trades.

q-fin.TR↗

arXiv2025

Optimal Exit Time for Liquidity Providers in Automated Market Makers

We study the problem of optimal liquidity withdrawal for a representative liquidity provider (LP) in an automated market maker (AMM). LPs earn fees from trading activity but are exposed to impermanent loss (IL) due to price fluctuations. While existing work has focused on static provision and exogenous exit strategies, we characterise the optimal exit time as the solution to a stochastic control problem with an endogenous stopping time. Mathematically, the LP's value function is shown to satisfy a Hamilton-Jacobi-Bellman quasi-variational inequality, for which we establish uniqueness in the viscosity sense. To solve the problem numerically, we develop two complementary approaches: a Euler scheme based on operator splitting and a Longstaff-Schwartz regression method. Calibrated simulations highlight how the LP's optimal exit strategy depends on the oracle price volatility, fee levels, and the behaviour of arbitrageurs and noise traders. Our results show that while arbitrage generates both fees and IL, the LP's optimal decision balances these opposing effects based on the pool state variables and price misalignments. Lastly, we find the optimal fee level for the representative LP when they play the exit strategy we derived. This work contributes to a deeper understanding of dynamic liquidity provision in AMMs and provides insights into the sustainability of passive LP strategies under different market regimes.

q-fin.TR↗

arXiv2025

Martingale Posterior Neural Networks for Fast Sequential Decision Making

We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model parameters, our methods adopt a predictive-first perspective based on martingale posteriors. In particular, we work directly with the one-step-ahead posterior predictive, which we parameterize with a neural network and update sequentially with incoming observations. This decouples Bayesian decision-making from parameter-space inference: we sample from the posterior predictive for decision making, and update the parameters of the posterior predictive via fast, frequentist Kalman-filter-like recursions. Our algorithms operate in a fully online, replay-free setting, providing principled uncertainty quantification without costly posterior sampling. Empirically, they achieve competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization, offering 10-100 times faster inference than classical Thompson sampling while maintaining comparable or superior decision performance.

cs.LG↗

arXiv2025

Nash Equilibrium between Brokers and Traders

We study the perfect information Nash equilibrium between a broker and her clients -- an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information, profitability, and inventory control in the trading strategies of the broker and the informed trader.

q-fin.TR↗

arXiv2025

Equilibrium Reward for Liquidity Providers in Automated Market Makers

We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representative LP is the follower. We derive approximate closed-form equilibrium solutions to the stochastic game and analyze the reward structure. Our findings suggest that under the equilibrium contract, LPs have incentives to add liquidity to the pool only when higher liquidity on average attracts more noise trading. The equilibrium contract depends on the external price, the pool reference price, and the pool reserves. Our framework offers insights into AMM design for maximizing order flow while ensuring LP profitability.

q-fin.TR↗

arXiv2025

A Simple Strategy to Deal with Toxic Flow

We model the trading activity between a broker and her clients (informed and uninformed traders) as an infinite-horizon stochastic control problem. We derive the broker's optimal dealing strategy in closed form and use this to introduce an algorithm that bypasses the need to calibrate individual parameters, so the dealing strategy can be executed in real-world trading environments. Finally, we characterise the discount in the price of liquidity a broker offers clients. The discount strikes the optimal balance between maximising the order flow from the broker's clients and minimising adverse selection losses to the informed traders.

q-fin.TR↗

arXiv2025

A unifying framework for generalised Bayesian online learning in non-stationary environments

We propose a unifying framework for methods that perform probabilistic online learning in non-stationary environments. We call the framework BONE, which stands for generalised (B)ayesian (O)nline learning in (N)on-stationary (E)nvironments. BONE provides a common structure to tackle a variety of problems, including online continual learning, prequential forecasting, and contextual bandits. The framework requires specifying three modelling choices: (i) a model for measurements (e.g., a neural network), (ii) an auxiliary process to model non-stationarity (e.g., the time since the last changepoint), and (iii) a conditional prior over model parameters (e.g., a multivariate Gaussian). The framework also requires two algorithmic choices, which we use to carry out approximate inference under this framework: (i) an algorithm to estimate beliefs (posterior distribution) about the model parameters given the auxiliary variable, and (ii) an algorithm to estimate beliefs about the auxiliary variable. We show how the modularity of our framework allows for many existing methods to be reinterpreted as instances of BONE, and it allows us to propose new methods. We compare experimentally existing methods with our proposed new method on several datasets, providing insights into the situations that make each method more suitable for a specific task. We provide a Jax open source library to facilitate the adoption of this framework.

stat.ML↗

arXiv2024

Market Making with Exogenous Competition

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.

q-fin.MF↗

arXiv2024

Outlier-robust Kalman Filtering through Generalised Bayes

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

stat.ML↗