arXiv subjects

Gabriel Turinici

Publications and source records attributed to Gabriel Turinici.

At least 19 recordsLinked to original sources

arXiv2026

Inferring Missing Trajectory Data with Temporal Convolutional Networks

Trajectory data collected in real-world settings is frequently incomplete due to sensor failure, communication loss, or occlusion. We address the task of \emph{trajectory inpainting}: reconstructing contiguous missing segments from observed context. We propose a Temporal Convolutional Network (TCN) with symmetric dilation that relaxes the standard causality constraint, allowing each time step to draw on both past and future observations, a property that is essential for inpainting, but absent from forecasting-oriented architectures. The model is trained with a composite loss that combines weighted mean squared error, boundary--continuity penalties, and a smoothness regularizer. Trained on a synthetic dataset of $1,000$ (train), $200$ (validation), and $300$ (test) two-dimensional trajectories with randomly placed 20% masked segments, the model achieves good R$^{2}$, MSE and MAE metrics.

cs.AI↗

arXiv2026

Physics-Informed Neural Networks for coupled stiff transport systems

Purpose: Physics-Informed Neural Networks (PINNs) struggle with stiff, regime-changing transport equations due to instability, loss imbalance, and violations of physical consistency. This paper investigates these failures through the Marshak wave equations - a canonical benchmark from radiative transport - where initial and boundary conditions differ by up to 12 orders of magnitude, and proposes targeted modifications to the standard PINN framework to overcome them. Design/methodology/approach: Three modifications are introduced: (1) a ScaledSigmoid final activation enforcing physical bounds and positivity of the unknowns; (2) a logarithmic MSE loss replacing the standard quadratic loss for initial and boundary conditions, enabling training across extreme scale disparities; and (3) explicit enforcement of global conservation laws derived from the governing equations as an additional physics loss term. Monte Carlo sampling with exponential time weighting is used throughout. Findings: The proposed framework successfully recovers the Marshak wave dynamics - including the hot, cold, and wave-front regions - in agreement with a reference Implicit Monte Carlo solution, with run times under 30 minutes. Ablation studies confirm that each ingredient is essential: linear activation, absence of the logarithmic loss, or removal of the PDE term each independently cause the method to fail qualitatively. Originality/value: This work identifies and resolves three concrete failure modes of standard PINNs on stiff hyperbolic systems with nonlinear coupling. The combination of bounded activations, scale-aware loss functions, and conservation law enforcement constitutes a novel and practically validated framework, with applicability to radiative transport and other coupled stiff PDE systems in engineering.

physics.comp-ph↗

arXiv2026

From Arbitrage Removal to Density Extraction: A Model-Free Framework for Short-Dated Options

We study risk-neutral density extraction from short-dated option chains. As expiry approaches, option premia decline and bid--ask spreads can be large relative to prices, making mid quotes particularly uninformative. Stale or asynchronous quotes may also generate potential static arbitrages, rendering standard procedures infeasible or unstable. We develop a model-free pipeline that treats bid-ask quotes as the primitive market constraint. The pipeline consists of two steps. First, a procedure called ``Arbitrage Removal Iterative Executable Strategy'' (ARIES) filters executable static arbitrage at quoted bid and ask prices under market-depth constraints. Second, the ``Smooth Entropic Density EXtraction'' (SEDEx) then recovers the density through a criterion leveraging smoothness and entropy under bid-ask constraints. We test the pipeline on synthetic Heston panels and short-dated SPX option data, sampled from a few hours to one week before expiry. Computation is fast and returns robust densities across various market conditions, including scheduled macroeconomic announcements. As an empirical application, we use the recovered densities to construct short dated implied-volatility smiles.

q-fin.CP↗

arXiv2026

Vanishing L2 regularization for the softmax Multi Armed Bandit

Multi Armed Bandit (MAB) algorithms are a cornerstone of reinforcement learning and have been studied both theoretically and numerically. One of the most commonly used implementation uses a softmax mapping to prescribe the optimal policy and served as the foundation for downstream algorithms, including REINFORCE. Distinct from vanilla approaches, we consider here the L2 regularized softmax policy gradient where a quadratic term is subtracted from the mean reward. Previous studies exploiting convexity failed to identify a suitable theoretical framework to analyze its convergence when the regularization parameter vanishes. We prove here theoretical convergence results and confirm empirically that this regime makes the L2 regularization numerically advantageous on standard benchmarks.

cs.LG↗

arXiv2026

Softmax gradient policy for variance minimization and risk-averse multi armed bandits

Algorithms for the Multi-Armed Bandit (MAB) problem play a central role in sequential decision-making and have been extensively explored both theoretically and numerically. While most classical approaches aim to identify the arm with the highest expected reward, we focus on a risk-aware setting where the goal is to select the arm with the lowest variance, favoring stability over potentially high but uncertain returns. To model the decision process, we consider a softmax parameterization of the policy; we propose a new algorithm to select the minimal variance (or minimal risk) arm and prove its convergence under natural conditions. The algorithm constructs an unbiased estimate of the objective by using two independent draws from the current's arm distribution. We provide numerical experiments that illustrate the practical behavior of these algorithms and offer guidance on implementation choices. The setting also covers general risk-aware problems where there is a trade-off between maximizing the average reward and minimizing its variance.

cs.LG↗

arXiv2025

Model-Free Deep Hedging with Transaction Costs and Light Data Requirements

Option pricing theory, such as the Black and Scholes (1973) model, provides an explicit solution to construct a strategy that perfectly hedges an option in a continuous-time setting. In practice, however, trading occurs in discrete time and often involves transaction costs, making the direct application of continuous-time solutions potentially suboptimal. Previous studies, such as those by Buehler et al. (2018), Buehler et al. (2019) and Cao et al. (2019), have shown that deep learning or reinforcement learning can be used to derive better hedging strategies than those based on continuous-time models. However, these approaches typically rely on a large number of trajectories (of the order of $10^5$ or $10^6$) to train the model. In this work, we show that using as few as 256 trajectories is sufficient to train a neural network that significantly outperforms, in the Geometric Brownian Motion framework, both the classical Black & Scholes formula and the Leland model, which is arguably one of the most effective explicit alternatives for incorporating transaction costs. The ability to train neural networks with such a small number of trajectories suggests the potential for more practical and simple implementation on real-time financial series.

q-fin.MF↗

arXiv2024

The impact of recovery rate heterogeneity in achieving herd immunity

Herd immunity is a critical concept in epidemiology, describing a threshold at which a sufficient proportion of a population is immune, either through infection or vaccination, thereby preventing sustained transmission of a pathogen. In the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to study infectious disease dynamics, the achievement of herd immunity depends on key parameters, including the transmission rate ($\beta$) and the recovery rate ($\gamma$), where $\gamma$ represents the inverse of the mean infectious period. While the transmission rate has received substantial attention, recent studies have underscored the significant role of $\gamma$ in determining the timing and sustainability of herd immunity. Additionally, it is becoming increasingly evident that assuming $\gamma$ as a constant parameter might oversimplify the dynamics, as variations in recovery times can reflect diverse biological, social, and healthcare-related factors. In this paper, we investigate how heterogeneity in the recovery rate affects herd immunity. We show empirically that the mean of the recovery rate is not a reliable metric for determining the achievement of herd immunity. Furthermore, we provide a theoretical result demonstrating that it is instead the mean recovery time, which is the mean of the inverse $1/\gamma$ of the recovery rate that is critical in deciding whether herd immunity is achievable within the SIR framework. A similar result is proved for the SEIR model. These insights have significant implications for public health interventions and theoretical modeling of epidemic dynamics.

q-bio.PE↗

arXiv2024

Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France

The vaccination against ongoing epidemics is seldom compulsory but remains one of the most classical means to fight epidemic propagation. However recent debates concerning the innocuity of vaccines and their risk with respect to the risk of the epidemic itself lead to severe vaccination campaign failures and new mass behaviors appeared driven by individual self-interest. Prompted by this context we analyze, in a Susceptible-Infected-Recovered (SIR) model, whether egocentric individuals can reach an equilibrium with the rest of the society. Using techniques from the "Mean Field Games" theory, we extend previous results and show that an equilibrium exists and characterizes completely the individual best vaccination strategy (with or without discounting). We also compare with a strategy based only on overall societal optimization and exhibit a situation with non-negative price of anarchy. Finally, we apply the theory to the 2009-2010 Influenza A (H1N1) vaccination campaign in France and hint that a group of individuals stopped vaccinating at levels that indicated a pessimistic perception of the risk of the vaccine.

q-bio.PE↗

arXiv2024

The Quantization Monte Carlo method for solving radiative transport equations

We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given simulation cell, the proposed method advances the time by replacing many collisions with sampling directly from the escape distribution of the particle. In order to perform the sampling, for each triplet of parameters (opacity, remaining time, initial position in the cell) on a parameter grid, the escape distribution is precomputed offline and only the quantiles are retained. The online computation samples only from this quantized (i.e., discrete) version by choosing a parameter triplet on the grid (close to actual particle's parameters) and returning at random one quantile from the precomputed set of quantiles for that parameter. We first check numerically that the escape laws depend smoothly on the parameters and then implement the procedure on a benchmark with good results.

physics.comp-ph↗

arXiv2024

Regime-Aware Time Weighting for Physics-Informed Neural Networks

We introduce a novel method to handle the time dimension when Physics-Informed Neural Networks (PINNs) are used to solve time-dependent differential equations; our proposal focuses on how time sampling and weighting strategies affect solution quality. While previous methods proposed heuristic time-weighting schemes, our approach is grounded in theoretical insights derived from the Lyapunov exponents, which quantify the sensitivity of solutions to perturbations over time. This principled methodology automatically adjusts weights based on the stability regime of the system -- whether chaotic, periodic, or stable. Numerical experiments on challenging benchmarks, including the chaotic Lorenz system and the Burgers' equation, demonstrate the effectiveness and robustness of the proposed method. Compared to existing techniques, our approach offers improved convergence and accuracy without requiring additional hyperparameter tuning. The findings underline the importance of incorporating causality and dynamical system behavior into PINN training strategies, providing a robust framework for solving time-dependent problems with enhanced reliability.

cs.LG↗

arXiv2024

Optimal time sampling in physics-informed neural networks

Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which includes, when the equation is time-dependent, a time sampling. It was argued in the literature that the sampling need not be uniform but should overweight initial time instants, but no rigorous explanation was provided for this choice. In the present work we take some prototypical examples and, under standard hypothesis concerning the neural network convergence, we show that the optimal time sampling follows a (truncated) exponential distribution. In particular we explain when is best to use uniform time sampling and when one should not. The findings are illustrated with numerical examples on linear equation, Burgers' equation and the Lorenz system.

cs.LG↗

arXiv2024

Model free collision aggregation for the computation of escape distributions

Motivated by a heat radiative transport equation, we consider a particle undergoing collisions in a space-time domain and propose a method to sample its escape time, space and direction from the domain. The first step of the procedure is an estimation of how many elementary collisions is safe to take before chances of exiting the domain are too high; then these collisions are aggregated into a single movement. The method does not use any model nor any particular regime of parameters. We give theoretical results both under the normal approximation and without it and test the method on some benchmarks from the literature. The results confirm the theoretical predictions and show that the proposal is an efficient method to sample the escape distribution of the particle.

physics.comp-ph↗

arXiv2024

Transformer for Times Series: an Application to the S&P500

The transformer models have been extensively used with good results in a wide area of machine learning applications including Large Language Models and image generation. Here, we inquire on the applicability of this approach to financial time series. We first describe the dataset construction for two prototypical situations: a mean reverting synthetic Ornstein-Uhlenbeck process on one hand and real S&P500 data on the other hand. Then, we present in detail the proposed Transformer architecture and finally we discuss some encouraging results. For the synthetic data we predict rather accurately the next move, and for the S&P500 we get some interesting results related to quadratic variation and volatility prediction.

cs.AI↗

arXiv2024

Convergence of a L2 regularized Policy Gradient Algorithm for the Multi Armed Bandit

Although Multi Armed Bandit (MAB) on one hand and the policy gradient approach on the other hand are among the most used frameworks of Reinforcement Learning, the theoretical properties of the policy gradient algorithm used for MAB have not been given enough attention. We investigate in this work the convergence of such a procedure for the situation when a $L2$ regularization term is present jointly with the 'softmax' parametrization. We prove convergence under appropriate technical hypotheses and test numerically the procedure including situations beyond the theoretical setting. The tests show that a time dependent regularized procedure can improve over the canonical approach especially when the initial guess is far from the solution.

stat.ML↗

arXiv2023

Onflow: a model free, online portfolio allocation algorithm robust to transaction fees

We introduce Onflow, a reinforcement learning method for optimizing portfolio allocation via gradient flows. Our approach dynamically adjusts portfolio allocations to maximize expected log returns while accounting for transaction costs. Using a softmax parameterization, Onflow updates allocations through an ordinary differential equation derived from gradient flow methods. This algorithm belongs to the large class of stochastic optimization procedures; we measure its efficiency by comparing our results to the mathematical theoretical values in a log-normal framework and to standard benchmarks from the 'old NYSE' dataset. For log-normal assets with zero transaction costs, Onflow replicates Markowitz optimal portfolio, achieving the best possible allocation. Numerical experiments from the 'old NYSE' dataset show that Onflow leads to dynamic asset allocation strategies whose performances are: a) comparable to benchmark strategies such as Cover's Universal Portfolio or Helmbold et al. ``multiplicative updates'' approach when transaction costs are zero, and b) better than previous procedures when transaction costs are high. Onflow can even remain efficient in regimes where other dynamical allocation techniques do not work anymore. Onflow is a promising portfolio management strategy that relies solely on observed prices, requiring no assumptions about asset return distributions. This makes it robust against model risk, offering a practical solution for real-world trading strategies.

q-fin.PM↗

arXiv2023

High order universal portfolios

The Cover universal portfolio (UP from now on) has many interesting theoretical and numerical properties and was investigated for a long time. Building on it, we explore what happens when we add this UP to the market as a new synthetic asset and construct by recurrence higher order UPs. We investigate some important theoretical properties of the high order UPs and show in particular that they are indeed different from the Cover UP and are capable to break the time permutation invariance. We show that under some perturbation regime the second high order UP has better Sharp ratio than the standard UP and briefly investigate arbitrage opportunities thus created. Numerical experiences on a benchmark from the literature confirm that high order UPs improve Cover's UP performances.

q-fin.PM↗

arXiv2023

Diversity in deep generative models and generative AI

The decoder-based machine learning generative algorithms such as Generative Adversarial Networks (GAN), Variational Auto-Encoders (VAE), Transformers show impressive results when constructing objects similar to those in a training ensemble. However, the generation of new objects builds mainly on the understanding of the hidden structure of the training dataset followed by a sampling from a multi-dimensional normal variable. In particular each sample is independent from the others and can repeatedly propose same type of objects. To cure this drawback we introduce a kernel-based measure quantization method that can produce new objects from a given target measure by approximating it as a whole and even staying away from elements already drawn from that distribution. This ensures a better diversity of the produced objects. The method is tested on classic machine learning benchmarks.

cs.CV↗

arXiv2023

Deep Conditional Measure Quantization

Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (in some metric space of probability measures). Various methods exists to do so, but the situation of quantizing a conditional law has been less explored. We propose a method, called DCMQ, involving a Huber-energy kernel-based approach coupled with a deep neural network architecture. The method is tested on several examples and obtains promising results.

stat.ML↗