arXiv subjects

Nick Firoozye

Publications and source records attributed to Nick Firoozye.

14 recordsLinked to original sources

arXiv2026

Adaptive Benign Overfitting (ABO): Overparameterized RLS for Online Learning in Non-stationary Time-series

Overparameterized models have recently challenged conventional learning theory by exhibiting improved generalization beyond the interpolation limit, a phenomenon known as benign overfitting. This work introduces Adaptive Benign Overfitting (ABO), extending the recursive least-squares (RLS) framework to this regime through a numerically stable formulation based on orthogonal-triangular updates. A QR-based exponentially weighted RLS (QR-EWRLS) algorithm is introduced, combining random Fourier feature mappings with forgetting-factor regularization to enable online adaptation under non-stationary conditions. The orthogonal decomposition prevents the numerical divergence associated with covariance-form RLS while retaining adaptability to evolving data distributions. Experiments on nonlinear synthetic time series confirm that the proposed approach maintains bounded residuals and stable condition numbers while reproducing the double-descent behavior characteristic of overparameterized models. Applications to forecasting foreign exchange and electricity demand show that ABO is highly accurate (comparable to baseline kernel methods) while achieving speed improvements of between 20 and 40 percent. The results provide a unified view linking adaptive filtering, kernel approximation, and benign overfitting within a stable online learning framework.

q-fin.ST↗

arXiv2025

When AI Trading Agents Compete: Adverse Selection of Meta-Orders by Reinforcement Learning-Based Market Making

We investigate the mechanisms by which medium-frequency trading agents are adversely selected by opportunistic high-frequency traders. We use reinforcement learning (RL) within a Hawkes Limit Order Book (LOB) model in order to replicate the behaviours of high-frequency market makers. In contrast to the classical models with exogenous price impact assumptions, the Hawkes model accounts for endogenous price impact and other key properties of the market (Jain et al. 2024a). Given the real-world impracticalities of the market maker updating strategies for every event in the LOB, we formulate the high-frequency market making agent via an impulse control reinforcement learning framework (Jain et al. 2025). The RL used in the simulation utilises Proximal Policy Optimisation (PPO) and self-imitation learning. To replicate the adverse selection phenomenon, we test the RL agent trading against a medium frequency trader (MFT) executing a meta-order and demonstrate that, with training against the MFT meta-order execution agent, the RL market making agent learns to capitalise on the price drift induced by the meta-order. Recent empirical studies have shown that medium-frequency traders are increasingly subject to adverse selection by high-frequency trading agents. As high-frequency trading continues to proliferate across financial markets, the slippage costs incurred by medium-frequency traders are likely to increase over time. However, we do not observe that increased profits for the market making RL agent necessarily cause significantly increased slippages for the MFT agent.

q-fin.TR↗

arXiv2025

An Impulse Control Approach to Market Making in a Hawkes LOB Market

We study the optimal Market Making problem in a Limit Order Book (LOB) market simulated using a high-fidelity, mutually exciting Hawkes process. Departing from traditional Brownian-driven mid-price models, our setup captures key microstructural properties such as queue dynamics, inter-arrival clustering, and endogenous price impact. Recognizing the realistic constraint that market makers cannot update strategies at every LOB event, we formulate the control problem within an impulse control framework, where interventions occur discretely via limit, cancel, or market orders. This leads to a high-dimensional, non-local Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJB-QVI), whose solution is analytically intractable and computationally expensive due to the curse of dimensionality. To address this, we propose a novel Reinforcement Learning (RL) approximation inspired by auxiliary control formulations. Using a two-network PPO-based architecture with self-imitation learning, we demonstrate strong empirical performance with limited training, achieving Sharpe ratios above 30 in a realistic simulated LOB. In addition to that, we solve the HJB-QVI using a deep learning method inspired by Sirignano and Spiliopoulos 2018 and compare the performance with the RL agent. Our findings highlight the promise of combining impulse control theory with modern deep RL to tackle optimal execution problems in jump-driven microstructural markets.

q-fin.TR↗

arXiv2025

(Non-Parametric) Bootstrap Robust Optimization for Portfolios and Trading Strategies

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter instability, and model misspecification. Traditional approaches, including parametric, bootstrap-based, and Bayesian methods, enhance stability by relying on confidence intervals or probabilistic priors but often impose restrictive assumptions. This study introduces a non-parametric bootstrap framework for robust optimization in financial decision-making. By resampling empirical data, the framework constructs flexible, data-driven confidence intervals without assuming specific distributional forms, thus capturing uncertainty in statistical estimates, model parameters, and utility functions. Treating utility as a random variable enables percentile-based optimization, naturally suited for risk-sensitive and worst-case decision-making. The approach aligns with recent advances in robust optimization, reinforcement learning, and risk-aware control, offering a unified perspective on robustness and generalization. Empirically, the framework mitigates overfitting and selection bias in trading strategy optimization and improves generalization in portfolio allocation. Results across portfolio and time-series momentum experiments demonstrate that the proposed method delivers smoother, more stable out-of-sample performance, offering a practical, distribution-free alternative to traditional robust optimization methods.

q-fin.ST↗

arXiv2024

Limit Order Book Simulations: A Review

Limit Order Books (LOBs) serve as a mechanism for buyers and sellers to interact with each other in the financial markets. Modelling and simulating LOBs is quite often necessary for calibrating and fine-tuning the automated trading strategies developed in algorithmic trading research. The recent AI revolution and availability of faster and cheaper compute power has enabled the modelling and simulations to grow richer and even use modern AI techniques. In this review we examine the various kinds of LOB simulation models present in the current state of the art. We provide a classification of the models on the basis of their methodology and provide an aggregate view of the popular stylized facts used in the literature to test the models. We additionally provide a focused study of price impact's presence in the models since it is one of the more crucial phenomena to model in algorithmic trading. Finally, we conduct a comparative analysis of various qualities of fits of these models and how they perform when tested against empirical data.

q-fin.TR↗

arXiv2023

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock's LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

q-fin.TR↗

arXiv2022

Online Learning with Radial Basis Function Networks

Financial time series are characterised by their nonstationarity and autocorrelation. Even if these time series are differenced, technically ensuring their stationarity, they experience regular covariate shifts and concept drifts. Against this backdrop, we combine feature representation transfer with sequential optimisation to provide multi-horizon returns forecasts. Our online learning rbfnet outperforms a random-walk baseline and several powerful batch learners. The rbfnets we formulate are naturally designed to measure the similarity between test samples and continuously updated prototypes that capture the characteristics of the feature space.

cs.CE↗

arXiv2022

Reinforcement Learning for Systematic FX Trading

We explore online inductive transfer learning, with a feature representation transfer from a radial basis function network formed of Gaussian mixture model hidden processing units to a direct, recurrent reinforcement learning agent. This agent is put to work in an experiment, trading the major spot market currency pairs, where we accurately account for transaction and funding costs. These sources of profit and loss, including the price trends that occur in the currency markets, are made available to the agent via a quadratic utility, who learns to target a position directly. We improve upon earlier work by targeting a risk position in an online transfer learning context. Our agent achieves an annualised portfolio information ratio of 0.52 with a compound return of 9.3\%, net of execution and funding cost, over a 7-year test set; this is despite forcing the model to trade at the close of the trading day at 5 pm EST when trading costs are statistically the most expensive.

q-fin.TR↗

arXiv2022

The Recurrent Reinforcement Learning Crypto Agent

We demonstrate a novel application of online transfer learning for a digital assets trading agent. This agent uses a powerful feature space representation in the form of an echo state network, the output of which is made available to a direct, recurrent reinforcement learning agent. The agent learns to trade the XBTUSD (Bitcoin versus US Dollars) perpetual swap derivatives contract on BitMEX on an intraday basis. By learning from the multiple sources of impact on the quadratic risk-adjusted utility that it seeks to maximise, the agent avoids excessive over-trading, captures a funding profit, and can predict the market's direction. Overall, our crypto agent realises a total return of 350\%, net of transaction costs, over roughly five years, 71\% of which is down to funding profit. The annualised information ratio that it achieves is 1.46.

cs.LG↗

arXiv2020

QuantNet: Transferring Learning Across Systematic Trading Strategies

Systematic financial trading strategies account for over 80% of trade volume in equities and a large chunk of the foreign exchange market. In spite of the availability of data from multiple markets, current approaches in trading rely mainly on learning trading strategies per individual market. In this paper, we take a step towards developing fully end-to-end global trading strategies that leverage systematic trends to produce superior market-specific trading strategies. We introduce QuantNet: an architecture that learns market-agnostic trends and use these to learn superior market-specific trading strategies. Each market-specific model is composed of an encoder-decoder pair. The encoder transforms market-specific data into an abstract latent representation that is processed by a global model shared by all markets, while the decoder learns a market-specific trading strategy based on both local and global information from the market-specific encoder and the global model. QuantNet uses recent advances in transfer and meta-learning, where market-specific parameters are free to specialize on the problem at hand, whilst market-agnostic parameters are driven to capture signals from all markets. By integrating over idiosyncratic market data we can learn general transferable dynamics, avoiding the problem of overfitting to produce strategies with superior returns. We evaluate QuantNet on historical data across 3103 assets in 58 global equity markets. Against the top performing baseline, QuantNet yielded 51% higher Sharpe and 69% Calmar ratios. In addition we show the benefits of our approach over the non-transfer learning variant, with improvements of 15% and 41% in Sharpe and Calmar ratios. Code available in appendix.

cs.LG↗

arXiv2019

Optimal Dynamic Strategies on Gaussian Returns

Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential weighted moving averages, forecasts from ARIMA models), we are able to derive closed-form expressions for the first four moments of the strategy's returns, in terms of correlations between the random signals and unknown future returns. By allowing for randomness in the asset-allocation and modelling the interaction of strategy weights with returns, we demonstrate that positive skewness and excess kurtosis are essential components of all positive Sharpe dynamic strategies, which is generally observed empirically; demonstrate that total least squares (TLS) or orthogonal least squares is more appropriate than OLS for maximizing the Sharpe ratio, while canonical correlation analysis (CCA) is similarly appropriate for the multi-asset case; derive standard errors on Sharpe ratios which are tighter than the commonly used standard errors from Lo; and derive standard errors on the skewness and kurtosis of strategies, apparently new results. We demonstrate these results are applicable asymptotically for a wide range of stationary time-series.

q-fin.PM↗

arXiv2019

Avoiding Backtesting Overfitting by Covariance-Penalties: an empirical investigation of the ordinary and total least squares cases

Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt to identify the appropriate parameters using historical data available, has been highly criticized due to the abundance of misleading results. Hence, there is an increasing interest in devising procedures for the assessment and comparison of strategies, that is, devising schemes for preventing what is known as backtesting overfitting. So far, many financial researchers have proposed different ways to tackle this problem that can be broadly categorised in three types: Data Snooping, Overestimated Performance, and Cross-Validation Evaluation. In this paper, we propose a new approach to dealing with financial overfitting, a Covariance-Penalty Correction, in which a risk metric is lowered given the number of parameters and data used to underpins a trading strategy. We outlined the foundation and main results behind the Covariance-Penalty correction for trading strategies. After that, we pursue an empirical investigation, comparing its performance with some other approaches in the realm of Covariance-Penalties across more than 1300 assets, using Ordinary and Total Least Squares. Our results suggest that Covariance-Penalties are a suitable procedure to avoid Backtesting Overfitting, and Total Least Squares provides superior performance when compared to Ordinary Least Squares.

q-fin.PM↗

arXiv2019

Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination

Systematic trading strategies are algorithmic procedures that allocate assets aiming to optimize a certain performance criterion. To obtain an edge in a highly competitive environment, the analyst needs to proper fine-tune its strategy, or discover how to combine weak signals in novel alpha creating manners. Both aspects, namely fine-tuning and combination, have been extensively researched using several methods, but emerging techniques such as Generative Adversarial Networks can have an impact into such aspects. Therefore, our work proposes the use of Conditional Generative Adversarial Networks (cGANs) for trading strategies calibration and aggregation. To this purpose, we provide a full methodology on: (i) the training and selection of a cGAN for time series data; (ii) how each sample is used for strategies calibration; and (iii) how all generated samples can be used for ensemble modelling. To provide evidence that our approach is well grounded, we have designed an experiment with multiple trading strategies, encompassing 579 assets. We compared cGAN with an ensemble scheme and model validation methods, both suited for time series. Our results suggest that cGANs are a suitable alternative for strategies calibration and combination, providing outperformance when the traditional techniques fail to generate any alpha.

cs.LG↗

arXiv2018

A Machine Learning-based Recommendation System for Swaptions Strategies

Derivative traders are usually required to scan through hundreds, even thousands of possible trades on a daily basis. Up to now, not a single solution is available to aid in their job. Hence, this work aims to develop a trading recommendation system, and apply this system to the so-called Mid-Curve Calendar Spread (MCCS), an exotic swaption-based derivatives package. In summary, our trading recommendation system follows this pipeline: (i) on a certain trade date, we compute metrics and sensitivities related to an MCCS; (ii) these metrics are feed in a model that can predict its expected return for a given holding period; and after repeating (i) and (ii) for all trades we (iii) rank the trades using some dominance criteria. To suggest that such approach is feasible, we used a list of 35 different types of MCCS; a total of 11 predictive models; and 4 benchmark models. Our results suggest that in general linear regression with lasso regularisation compared favourably to other approaches from a predictive and interpretability perspective.

q-fin.PM↗