algorithmic trading teams

Abstract: Classical theory predicts that irrational traders lose money to rational traders and are eventually driven out of the market. Yet noise trading, herding, and heuristic trading persist even in highly developed markets. We model a financial market as an ecology of two trading-behavior types, relatively rational (R) and boundedly rational (N), whose composition evolves under replicator dynamics according to relative performance. Each type's fitness depends on the share of the other type and on frictions. When the interaction is complementary, that is, rational traders profit from the mispricing created by boundedly rational traders while the latter benefit from the liquidity and price correction supplied by the former, and when the difference in frictions is moderate, a unique interior composition exists and is globally asymptotically stable: bounded rationality persists endogenously. When the interaction is antagonistic, the same point becomes a tipping threshold between two one-type regimes. Comparative statics show that lowering the costs of disciplined trading, as algorithmic and AI-based trading does, shifts the composition toward rational trading continuously but does not eliminate bounded rationality unless the cost advantage exceeds an explicit threshold.

Abstract: We study equilibrium learning in discretized Bayesian games, focusing on first-price auctions as a testbed for gradient-based learning dynamics under private information. While the symmetric independent private values model admits a unique Bayesian correlated equilibrium (BCE) in the continuous limit, standard convergence guarantees for gradient-based learners do not apply: classical no-regret theory predicts convergence only to Bayesian coarse correlated equilibria (BCCE), which can remain large and far from the competitive equilibrium even under fine discretizations. To bridge this gap, we introduce the notion of Bayesian semicoarse correlated equilibrium (BSCCE), an equilibrium concept that refines BCCE by restricting deviations to probability-preserving transformations consistent with projected gradient dynamics. We provide a linear programming characterization of BSCCE with polynomially many variables and constraints and establish the inclusion hierarchy $BCE \subseteq BSCCE \subseteq BCCE$. Our main finding is that the BSCCE set contracts in many cases as the discretization of the Bayesian game is refined. Even with priors for which BCCE fails to concentrate, the diameter of the BSCCE polytope shrinks toward zero, indicating convergence to the unique continuous-game Bayes-Nash equilibrium. These results provide a principled explanation for the observed robustness of gradient-based learning in discretized Bayesian games, showing that these dynamics select a smaller equilibrium set than standard no-regret theory predicts.

Abstract: Replicator dynamics, the central model of evolutionary game theory, describe populations evolving under selection and agents learning by trial and error. They also admit a third use: continuous-time Bayesian inference, in which an agent planning against an opponent accumulates evidence for each candidate strategy. Here we show that this use divides all two-player games into two classes. With the standard expected-utility payoff, the dynamics can be expressed as Bayesian updating only in games (with any number of actions) where no player has a dominant strategy. The logarithmic payoff of Ay and Erb admits the Bayesian representation in every game. Coordination, anti-coordination, and cyclic games share qualitative dynamics under both payoff definitions, with equilibria displaced and selection thresholds shifted. In contrast, the flows of every game with a dominant strategy are reversed between the payoff definitions, with the strictly dominant strategy eliminated under logarithmic payoffs. Cooperation therefore emerges in the Prisoner's Dilemma, and games of common interest converge to mutual defection. For two-action games the classification is complete and rests on an exact Hamiltonian structure shared by both payoff definitions. The structure gives a behavioural test: cycles in the classic Matching Pennies game have amplitude-independent period (isochronous) under logarithmic payoffs, but not under expected utility. Logarithmic evidence integration thus determines which strategic outcomes dynamical selection can reach, wherever learning approximates Bayesian updating.

Abstract: Recent advances in Generative AI have substantially improved financial sentiment analysis through post-trained financial large language models (LLMs). However, existing approaches remain confined to predicting the sentiment of each article in isolation and operate as black boxes, which limits contextual understanding and hinders deployment in high-stakes financial decision-making. To this end, we introduce FinLLM-KG, a model-agnostic framework that combines causal LLMs with a financial knowledge graph, in order to inject temporally grounded, company-level knowledge from SEC 10-K filings at inference time, without updating model weights. Within FinLLM-KG, context is supplied either as a natural-language company profile or as a small set of relevance-ranked factual triples. This enables sentiment predictions to account for broader firm-level information rather than the article alone, at almost zero computational cost and for any causal LLM. In addition, attributing each article-level sentiment score to individual sentences and to the retrieved knowledge-graph facts makes the evidence behind the prediction inspectable, thereby enhancing explainability and supporting human-in-the-loop review. Simulations demonstrate that FinLLM-KG consistently improves portfolio performance over the state-of-the-art baseline.

Abstract: A market maker provides liquidity by quoting prices to buy and sell an asset, earning the spread while managing inventory risk. We study market makers trained with multi-agent reinforcement learning on prediction markets, specifically Polymarket, whose thin order books pose distinct challenges. Three challenges underpin this research: adverse selection may cause a policy trained on real data to stop quoting; the consequences of a quote can arrive many steps after the action; and prediction-market L2 data does not identify individual orders needed for simulation. We address these challenges by reconstructing order-level LOBSTER-format data from Polymarket and training agents in JaxMARL-HFT on 417 real markets. We enrich the baseline market maker's observation space with the book and recent flow, redesign its actions and inventory controls, and propose a cooperative multi-agent decomposition into a quoter and a risk manager trained using recurrent Independent Proximal Policy Optimisation (IPPO) with RNN policies. We investigate reward shaping, particularly reward blending and post-fill markout, to mitigate credit-assignment difficulties between the agents. Our redesigned single-agent market maker quotes more frequently and incurs smaller held-out losses than the retrained JaxMARL-HFT baseline, although the contributions of jointly changed observations, actions and risk constraints are not separately identified. Decomposition alone performs poorly; careful reward design substantially improves the desk relative to the unshaped split and yields our best result. Models are evaluated on realised end-of-episode portfolio value on held-out markets. None establishes positive average portfolio value in periodic held-out evaluation, and each configuration was trained with one seed. The environment, data and protocol lay a foundation for makers that quote many linked markets at once.

Abstract: We study online learning in market making, where, at each round, a market maker posts bid and ask prices before observing the market price and the private valuation of an incoming trader. In this setting, Maran et al. 2026 introduce a feedback model motivated by limit order books, in which the trader's valuation is revealed only if no transaction occurs. Assuming that trader valuations are drawn i.i.d. from an unknown distribution while market prices are chosen adversarially, they establish an expected regret bound of $\widetilde{\mathcal{O}}(T^{2/3})$. In this work, we improve upon this guarantee by establishing a high-probability regret bound of $\widetilde{\mathcal{O}}(\sqrt{T})$. As a warm-up, we first consider the full-feedback setting. We introduce a discretization of the bid-ask space based on two coupled grids and combine it with Hedge to achieve the desired regret rate. Building on these ideas, we then address the substantially weaker feedback induced by a limit order book and develop an algorithm that achieves the same guarantee. Finally, we investigate the limits of learnability in fully adversarial environments, where the valuations may vary arbitrarily as well. Perhaps surprisingly, we show that when both market prices and trader valuations are chosen adversarially, sublinear regret is impossible even under full feedback, thereby motivating our stochastic assumption on the valuations.

Abstract: We study an online trading problem where a trader, given a sequence of i.i.d. prices drawn from a known distribution $F$ on $[0,1]$, must make irrevocable buy, sell, or hold decisions subject to storage constraints. We investigate achievable algorithmic performance measured in terms of regret, the difference between the expected profit of the hindsight optimal policy that knows the entire price sequence and an online algorithm. We analyze finite atomic and continuous distributions characterized by their local behavior around the median which we capture using a parameter $β$. The parameter $β$ quantifies how the mass of prices accumulates around the distribution median. We identify a new driver of algorithmic performance, demonstrating that median gaps coupled with an initial inventory level of zero can force regret scaling of $Ω(T^{(β+ 1)/(2β+4)})$ --- establishing a novel spectrum of fundamental limits on algorithmic performance. We then study STARS, short for Storage Trading by Averaging Repeatedly across multiple Scenarios, which simulates possible future price scenarios to approximate the value-to-go function and make buy/sell/hold decisions. We show that STARS obtain near-optimal algorithmic performance (upto poly-logarithmic factors) across a broad range of distributions. In particular, it achieves $O(\log T)$ regret for finite atomic prices, $\widetilde{O}(T^{β/(2β+2)})$ for continuous distributions without a median gap and $\widetilde{O}(T^{(β+1)/(2β+4)})$ for continuous distributions with a median gap for $β\geq 0$.

Abstract: A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing to a fixed action. Motivated by the problem of regulating algorithmic collusion, this refinement was introduced by Hartline, Wang, and Zhang [EC'26], who showed that it can be computed in polynomial time in explicitly represented normal-form game. In this paper, we examine the complexity of IVF(C)CEs in succinct games, which model more realistic strategic interactions that feature either many players or exponentially many pure strategies. We first show that computing an information-value-free CE is PPAD-complete in many-player polymatrix games or two-player Bayesian games, even when the approximation is a constant. We also prove an unconditional exponential query lower bound. Our results establish that IVFCEs are intractable, even in the centralized model, and rule out the existence of any efficient learning dynamics. This significantly strengthens the impossibility result of Hartline, Wang, and Zhang, which concerns a particular class of learning algorithms, and furnishes strong computational critiques of recent regulation on algorithmic collusion. To sidestep these hardness results, we examine the complexity of information-value-free CCE. Certain no-regret algorithms---such as regret matching or FTRL---provide a fully polynomial-time approximation scheme (FPTAS) for this problem. The complexity when the approximation is exponentially small turns out to be nuanced. On the one hand, leveraging no-regret dynamics, we establish membership in $\text{CLS} = \text{PPAD} \cap \text{PLS}$. On the other hand, we show that it is at least as hard as the P-matrix linear complementarity problem, and hence as hard as simple stochastic games. This shows that even IVFCCEs are unlikely to admit a polynomial-time algorithm barring a major breakthrough.

Abstract: We introduce Multiplicatively Optimistic Regret Matching (MORM), an uncoupled learning rule for finite general-sum games. Under simultaneous full-information self-play, every player achieves external regret $O(\sqrt n\log d)$ uniformly over all horizons, using only one-step optimism. The analysis combines a potential-based regret-matching argument with multiplicative stability and Hellinger control of strategy movement. A learning-rate safeguard additionally gives $O(\sqrt{T\log d})$ regret in the face of adversarial utilities.

Abstract: Stock price prediction remains challenging due to the non-stationary and noisy nature of financial time series. Existing deep learning models often rely on rigid decision-level fusion, ad hoc hyperparameter tuning, and compressed final-layer outputs, causing information loss, overfitting, and limited cross-market generalization. We propose VertiFuseX, a hybrid LSTM architecture using penultimate-layer vertical fusion of multi-scale temporal representations. VertiFuseX stacks and reweights penultimate features from LSTM, Bi-LSTM, and St-LSTM branches, integrates a parallel DNN stream, and jointly optimizes all components via backpropagation under a fixed hyperparameter configuration. This preserves richer intermediate temporal information across scales. Evaluated on 15 years (2010-2024) of closing prices from 10 global equity indices using strict chronological out-of-sample testing with the final 365 trading days held out, VertiFuseX achieves 30-54% MAPE reductions and over 40% improvements in MAE and RMSE versus LSTM-based baselines, and outperforms seven state-of-the-art models across 33 metric-dataset comparisons. Ablation studies confirm penultimate-layer fusion drives these gains over final-layer fusion and decision-level ensembling. Gradient-based saliency analysis shows consistent emphasis on mid-range dependencies at lags 9-15 days. Economic validation via algorithmic trading simulation under extreme market regimes shows reduced maximum drawdowns and superior risk-adjusted returns. With 675k parameters, a 2.6 MB memory footprint, and 1.5 ms/sample inference latency, VertiFuseX offers a lightweight, interpretable, deployment-ready framework for robust financial forecasting.