General Equities

A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications ArXiv ID: 2512.03123 “View on arXiv” Authors: Amit Kumar Jha Abstract This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols. ...

Noise estimation of SDE from a single data trajectory ArXiv ID: 2509.25484 “View on arXiv” Authors: Munawar Ali, Purba Das, Qi Feng, Liyao Gao, Guang Lin Abstract In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transformations, and using the drift function’s initial value as input, we construct drift estimators while simultaneously recovering the model noise. This allows us to recover the underlying $\mathbb P$ Brownian motion increments. Building on these estimators, we introduce the first stochastic Sparse Identification of Stochastic Differential Equation (SSISDE) algorithm, capable of identifying the governing SDE dynamics from a single observed trajectory without requiring ergodicity or stationarity. To validate the proposed approach, we conduct numerical experiments with both linear and quadratic drift-diffusion functions. Among these, the Black-Scholes SDE is included as a representative case of a system that does not satisfy ergodicity or stationarity. ...

Reinforcement Learning-Based Market Making as a Stochastic Control on Non-Stationary Limit Order Book Dynamics ArXiv ID: 2509.12456 “View on arXiv” Authors: Rafael Zimmer, Oswaldo Luiz do Valle Costa Abstract Reinforcement Learning has emerged as a promising framework for developing adaptive and data-driven strategies, enabling market makers to optimize decision-making policies based on interactions with the limit order book environment. This paper explores the integration of a reinforcement learning agent in a market-making context, where the underlying market dynamics have been explicitly modeled to capture observed stylized facts of real markets, including clustered order arrival times, non-stationary spreads and return drifts, stochastic order quantities and price volatility. These mechanisms aim to enhance stability of the resulting control agent, and serve to incorporate domain-specific knowledge into the agent policy learning process. Our contributions include a practical implementation of a market making agent based on the Proximal-Policy Optimization (PPO) algorithm, alongside a comparative evaluation of the agent’s performance under varying market conditions via a simulator-based environment. As evidenced by our analysis of the financial return and risk metrics when compared to a closed-form optimal solution, our results suggest that the reinforcement learning agent can effectively be used under non-stationary market conditions, and that the proposed simulator-based environment can serve as a valuable tool for training and pre-training reinforcement learning agents in market-making scenarios. ...

On a multivariate extension for Copula-based Conditional Value at Risk ArXiv ID: 2508.16132 “View on arXiv” Authors: Andres Mauricio Molina Barreto Abstract Copula-based Conditional Value at Risk (CCVaR) is defined as an alternative version of the classical Conditional Value at Risk (CVaR) for multivariate random vectors intended to be real-valued. We aim to generalize CCVaR to several dimensions (d>=2) when the dependence structure is given by an Archimedean copula. While previous research focused on the bivariate case, leaving the multivariate version unexplored, an almost closed-form expression for CCVaR under an Archimedean copula is derived. The conditions under which this risk measure satisfies coherence are then examined. Finally, numerical experiments based on real data are conducted to estimate CCVaR, and the results are compared with classical measures of Value at Risk (VaR) and Conditional Value at Risk (CVaR). ...

CNN-DRL with Shuffled Features in Finance ArXiv ID: 2402.03338 “View on arXiv” Authors: Unknown Abstract In prior methods, it was observed that the application of Convolutional Neural Networks agent in Deep Reinforcement Learning to financial data resulted in an enhanced reward. In this study, a specific permutation was applied to the feature vector, thereby generating a CNN matrix that strategically positions more pertinent features in close proximity. Our comprehensive experimental evaluations unequivocally demonstrate a substantial enhancement in reward attainment. ...

Almost Perfect Shadow Prices ArXiv ID: 2401.00970 “View on arXiv” Authors: Unknown Abstract Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price Ansatz for maximizing long term returns given average volatility yields a strategy that is, for small bid-ask-spreads, asymptotically optimal at third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices. ...