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Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most…
Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate…
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical…
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…
We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity…
A common assumption in machine learning is that samples are independently and identically distributed (i.i.d). However, the contributions of different samples are not identical in training. Some samples are difficult to learn and some…
Can large language models (LLMs) generate continuous numerical features that improve reinforcement learning (RL) trading agents? We build a modular pipeline where a frozen LLM serves as a stateless feature extractor, transforming…
The gloabal objective of inverse Reinforcement Learning (IRL) is to estimate the unknown cost function of some MDP base on observed trajectories generated by (approximate) optimal policies. The classical approach consists in tuning this…
To predict the future movements of stock markets, numerous studies concentrate on daily data and employ various machine learning (ML) models as benchmarks that often vary and lack standardization across different research works. This paper…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
We introduce a novel framework for analyzing reinforcement learning (RL) in continuous state-action spaces, and use it to prove fast rates of convergence in both off-line and on-line settings. Our analysis highlights two key stability…
The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences…
The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the $\mathcal{L}_2$-gain concept. However, recent research has pointed out that…
We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence…
Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. This problem has gained increasing attention in recent years, and efforts to improve it have grown substantially. To aid RL researchers and production…
We consider a general class of high-volume, fast-moving production-inventory systems based on both lost-sales and backorder inventory models. Such systems require a fundamental understanding of the asymptotic behavior of key performance…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
Inverse reinforcement learning (IRL), which infers reward functions from demonstrations, is a valuable tool for modeling and understanding decision-making behavior. Many variants of IRL have been developed to capture complexities of human…
A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…