Learning to Manage Investment Portfolios beyond Simple Utility Functions ArXiv ID: 2510.26165 “View on arXiv” Authors: Maarten P. Scholl, Mahmoud Mahfouz, Anisoara Calinescu, J. Doyne Farmer Abstract While investment funds publicly disclose their objectives in broad terms, their managers optimize for complex combinations of competing goals that go beyond simple risk-return trade-offs. Traditional approaches attempt to model this through multi-objective utility functions, but face fundamental challenges in specification and parameterization. We propose a generative framework that learns latent representations of fund manager strategies without requiring explicit utility specification. Our approach directly models the conditional probability of a fund’s portfolio weights, given stock characteristics, historical returns, previous weights, and a latent variable representing the fund’s strategy. Unlike methods based on reinforcement learning or imitation learning, which require specified rewards or labeled expert objectives, our GAN-based architecture learns directly from the joint distribution of observed holdings and market data. We validate our framework on a dataset of 1436 U.S. equity mutual funds. The learned representations successfully capture known investment styles, such as “growth” and “value,” while also revealing implicit manager objectives. For instance, we find that while many funds exhibit characteristics of Markowitz-like optimization, they do so with heterogeneous realizations for turnover, concentration, and latent factors. To analyze and interpret the end-to-end model, we develop a series of tests that explain the model, and we show that the benchmark’s expert labeling are contained in our model’s encoding in a linear interpretable way. Our framework provides a data-driven approach for characterizing investment strategies for applications in market simulation, strategy attribution, and regulatory oversight. ...

RL-Exec: Impact-Aware Reinforcement Learning for Opportunistic Optimal Liquidation, Outperforms TWAP and a Book-Liquidity VWAP on BTC-USD Replays ArXiv ID: 2511.07434 “View on arXiv” Authors: Enzo Duflot, Stanislas Robineau Abstract We study opportunistic optimal liquidation over fixed deadlines on BTC-USD limit-order books (LOB). We present RL-Exec, a PPO agent trained on historical replays augmented with endogenous transient impact (resilience), partial fills, maker/taker fees, and latency. The policy observes depth-20 LOB features plus microstructure indicators and acts under a sell-only inventory constraint to reach a residual target. Evaluation follows a strict time split (train: Jan-2020; test: Feb-2020) and a per-day protocol: for each test day we run ten independent start times and aggregate to a single daily score, avoiding pseudo-replication. We compare the agent to (i) TWAP and (ii) a VWAP-like baseline allocating using opposite-side order-book liquidity (top-20 levels), both executed on identical timestamps and costs. Statistical inference uses one-sided Wilcoxon signed-rank tests on daily RL-baseline differences with Benjamini-Hochberg FDR correction and bootstrap confidence intervals. On the Feb-2020 test set, RL-Exec significantly outperforms both baselines and the gap increases with the execution horizon (+2-3 bps at 30 min, +7-8 bps at 60 min, +23 bps at 120 min). Code: github.com/Giafferri/RL-Exec ...

A mathematical study of the excess growth rate ArXiv ID: 2510.25740 “View on arXiv” Authors: Steven Campbell, Ting-Kam Leonard Wong Abstract We study the excess growth rate – a fundamental logarithmic functional arising in portfolio theory – from the perspective of information theory. We show that the excess growth rate can be connected to the Rényi and cross entropies, the Helmholtz free energy, L. Campbell’s measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen’s inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance. ...

Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures ArXiv ID: 2510.24607 “View on arXiv” Authors: Yimeng Qiu Abstract We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the benchmark and targets satisfy convex-hull conditions. We derive the dual concave formulation with explicit gradient, Hessian, and sensitivity expressions, and provide two provably convergent solvers: a damped dual Newton method with global convergence and local quadratic rate, and a KL-projection scheme based on iterative proportional fitting and Bregman-Dykstra projections. We further generalize EGMU to handle elastic targets and robust target sets, and introduce a path-following ordinary differential equation for tracing solution trajectories. Stable and scalable implementations are provided using LogSumExp stabilization, covariance regularization, and half-space KL projections. Our focus is on theory and reproducible algorithms; empirical benchmarking is optional. ...

Explainable Federated Learning for U.S. State-Level Financial Distress Modeling ArXiv ID: 2511.08588 “View on arXiv” Authors: Lorenzo Carta, Fernando Spadea, Oshani Seneviratne Abstract We present the first application of federated learning (FL) to the U.S. National Financial Capability Study, introducing an interpretable framework for predicting consumer financial distress across all 50 states and the District of Columbia without centralizing sensitive data. Our cross-silo FL setup treats each state as a distinct data silo, simulating real-world governance in nationwide financial systems. Unlike prior work, our approach integrates two complementary explainable AI techniques to identify both global (nationwide) and local (state-specific) predictors of financial hardship, such as contact from debt collection agencies. We develop a machine learning model specifically suited for highly categorical, imbalanced survey data. This work delivers a scalable, regulation-compliant blueprint for early warning systems in finance, demonstrating how FL can power socially responsible AI applications in consumer credit risk and financial inclusion. ...

The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets ArXiv ID: 2511.05523 “View on arXiv” Authors: Ciaran O’Connor, Mohamed Bahloul, Steven Prestwich, Andrea Visentin Abstract Electricity price forecasting has become a critical tool for decision-making in energy markets, particularly as the increasing penetration of renewable energy introduces greater volatility and uncertainty. Historically, research in this field has been dominated by point forecasting methods, which provide single-value predictions but fail to quantify uncertainty. However, as power markets evolve due to renewable integration, smart grids, and regulatory changes, the need for probabilistic forecasting has become more pronounced, offering a more comprehensive approach to risk assessment and market participation. This paper presents a review of probabilistic forecasting methods, tracing their evolution from Bayesian and distribution based approaches, through quantile regression techniques, to recent developments in conformal prediction. Particular emphasis is placed on advancements in probabilistic forecasting, including validity-focused methods which address key limitations in uncertainty estimation. Additionally, this review extends beyond the Day-Ahead Market to include the Intra-Day and Balancing Markets, where forecasting challenges are intensified by higher temporal granularity and real-time operational constraints. We examine state of the art methodologies, key evaluation metrics, and ongoing challenges, such as forecast validity, model selection, and the absence of standardised benchmarks, providing researchers and practitioners with a comprehensive and timely resource for navigating the complexities of modern electricity markets. ...

The Omniscient, yet Lazy, Investor ArXiv ID: 2510.24467 “View on arXiv” Authors: Stanisław M. S. Halkiewicz Abstract We formalize the paradox of an omniscient yet lazy investor - a perfectly informed agent who trades infrequently due to execution or computational frictions. Starting from a deterministic geometric construction, we derive a closed-form expected profit function linking trading frequency, execution cost, and path roughness. We prove existence and uniqueness of the optimal trading frequency and show that this optimum can be interpreted through the fractal dimension of the price path. A stochastic extension under fractional Brownian motion provides analytical expressions for the optimal interval and comparative statics with respect to the Hurst exponent. Empirical illustrations on equity data confirm the theoretical scaling behavior. ...

Adaptive Multilevel Splitting: First Application to Rare-Event Derivative Pricing ArXiv ID: 2510.23461 “View on arXiv” Authors: Riccardo Gozzo Abstract This work investigates the computational burden of pricing binary options in rare event regimes and introduces an adaptation of the adaptive multilevel splitting (AMS) method for financial derivatives. Standard Monte Carlo becomes inefficient for deep out-of-the-money binaries due to discontinuous payoffs and extremely small exercise probabilities, requiring prohibitively large sample sizes for accurate estimation. The proposed AMS framework reformulates the rare-event problem as a sequence of conditional events and is applied under both Black-Scholes and Heston dynamics. Numerical experiments cover European, Asian, and up-and-in barrier digital options, together with a multidimensional digital payoff designed as a stress test. Across all contracts, AMS achieves substantial gains, reaching up to 200-fold improvements over standard Monte Carlo, while preserving unbiasedness and showing robust performance with respect to the choice of importance function. To the best of our knowledge, this is the first application of AMS to derivative pricing. An open-source Rcpp implementation is provided, supporting multiple discretisation schemes and alternative importance functions. ...

An uncertainty-aware physics-informed neural network solution for the Black-Scholes equation: a novel framework for option pricing ArXiv ID: 2511.05519 “View on arXiv” Authors: Sina Kazemian, Ghazal Farhani, Amirhessam Yazdi Abstract We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black–Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over $(S,t)$. The model embeds the BS operator and boundary/terminal conditions in a residual-based objective and requires no labeled prices. For American options, early exercise is handled via an obstacle-style relaxation while retaining the BS residual in the continuation region. To quantify \emph{“epistemic”} uncertainty, we introduce an anchored-ensemble fine-tuning stage (AT–PINN) that regularizes each model toward a sampled anchor and yields prediction bands alongside point estimates. On European calls/puts, the approach attains low errors (e.g., MAE $\sim 5\times10^{"-2"}$, RMSE $\sim 7\times10^{"-2"}$, explained variance $\approx 0.999$ in representative settings) and tracks ground truth closely across strikes and maturities. For American puts, the method remains accurate (MAE/RMSE on the order of $10^{"-1"}$ with EV $\approx 0.999$) and does not exhibit the error accumulation associated with time-marching schemes. Against data-driven baselines (ANN, RNN) and a Kolmogorov–Arnold FINN variant (KAN), our PINN matches or outperforms on accuracy while training more stably; anchored ensembles provide uncertainty bands that align with observed error scales. We discuss design choices (loss balancing, sampling near the payoff kink), limitations, and extensions to higher-dimensional BS settings and alternative dynamics. ...

Building Trust in Illiquid Markets: an AI-Powered Replication of Private Equity Funds ArXiv ID: 2510.23201 “View on arXiv” Authors: E. Benhamou, JJ. Ohana, B. Guez, E. Setrouk, T. Jacquot Abstract In response to growing demand for resilient and transparent financial instruments, we introduce a novel framework for replicating private equity (PE) performance using liquid, AI-enhanced strategies. Despite historically delivering robust returns, private equity’s inherent illiquidity and lack of transparency raise significant concerns regarding investor trust and systemic stability, particularly in periods of heightened market volatility. Our method uses advanced graphical models to decode liquid PE proxies and incorporates asymmetric risk adjustments that emulate private equity’s unique performance dynamics. The result is a liquid, scalable solution that aligns closely with traditional quarterly PE benchmarks like Cambridge Associates and Preqin. This approach enhances portfolio resilience and contributes to the ongoing discourse on safe asset innovation, supporting market stability and investor confidence. ...