arXiv subjects

Matteo Garbelli

Publications and source records attributed to Matteo Garbelli.

6 recordsLinked to original sources

arXiv2026

Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs

We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form of a Generalized BSDE. We establish the connection between this FBSDE system and non-linear path-dependent PDEs with Neumann boundary conditions by deriving a representation formula.

math.PR↗

arXiv2026

Data-Driven Stochastic VRP: Integration of Forecast Duration into Optimization for Utility Workforce Management

This paper investigates the integration of machine learning forecasts of intervention durations into a stochastic variant of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). In particular, we exploit tree-based gradient boosting (XGBoost) trained on eight years of gas meter maintenance data to produce point predictions and uncertainty estimates, which then drive a multi-objective evolutionary optimization routine. The methodology addresses uncertainty through sub-Gaussian concentration bounds for route-level risk buffers and explicitly accounts for competing operational KPIs through a multi-objective formulation. Empirical analysis of prediction residuals validates the sub-Gaussian assumption underlying the risk model. From an empirical point of view, our results report improvements around 20-25\% in operator utilization and completion rates compared with plans computed using default durations. The integration of uncertainty quantification and risk-aware optimization provides a practical framework for handling stochastic service durations in real-world routing applications.

math.OC↗

arXiv2024

Reinforcement Learning for Bidding Strategy Optimization in Day-Ahead Energy Market

In a day-ahead market, energy buyers and sellers submit their bids for a particular future time, including the amount of energy they wish to buy or sell and the price they are prepared to pay or receive. However, the dynamic for forming the Market Clearing Price (MCP) dictated by the bidding mechanism is frequently overlooked in the literature on energy market modelling. Forecasting models usually focus on predicting the MCP rather than trying to build the optimal supply and demand curves for a given price scenario. Following this approach, the article focuses on developing a bidding strategy for a seller in a continuous action space through a single agent Reinforcement Learning algorithm, specifically the Deep Deterministic Policy Gradient. The algorithm controls the offering curve (action) based on past data (state) to optimize future payoffs (rewards). The participant can access historical data on production costs, capacity, and prices for various sources, including renewable and fossil fuels. The participant gains the ability to operate in the market with greater efficiency over time to maximize individual payout.

math.OC↗

arXiv2022

Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations

We consider a system of Forward Backward Stochastic Differential Equations (FBSDEs), with time delayed generator and driven by L\`evy-type noise. We establish a non linear Feynman Kac representation formula associating the solution given by the FBSDEs-system to the solution of a path dependent nonlinear Kolmogorov equation with both delay and jumps. Obtained results are then applied to study a generalization of the so-called Large Investor Problem where the stock price evolves according to a jump-diffusion dynamic.

math.PR↗

arXiv2022

The Master Equation in a Bounded Domain with Absorption

We analyze the Master Equation within Mean Field Games (MFG) theory considering a bounded domain with homogeneous Dirichlet conditions. Concerning the N-players differential game, the player's dynamic ends when touching the boundary. We analyze the well-posedness of the Master Equation and the regularity of its solutions for a suitable class of parabolic equations.

math.AP↗

arXiv2020

Time-Delayed Generalized BSDEs

We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing continuous stochastic process. Moreover, we obtain a result of continuity of the solution with regard to the increasing process, assuming only uniform convergence, but not in variation. We also prove the existence in the case of an arbitrary delay by imposing monotonicity and linearity on generators. Lastly, we provide an application of the theoretical framework within an insurance based example.

math.PR↗