Research

Research Interests: Optimal control problems, Dynamic Programming approach, first and second order Hamilton-Jacobi equations, numerical schemes for Hamilton-Jacobi equations, computational finance.

PhD in Applied Mathematics (April 2015), ENSTA ParisTech, Université Paris-Saclay

ITN SADCO project fellow 2011-2014, INRIA Saclay Ile de France

Thesis: On some stochastic control problems under state constraints

Supervisors: Hasnaa Zidani and Olivier Bokanowski

Preprints:

A deep solver for BSDEs with jumps (with A. Gnoatto and M. Patacca). Preprint.

Publications in peer-reviewed journals:

Deep xVA solver-A neural network based counterparty credit risk management framework (with A. Gnoatto and C. Reisinger). Forthcoming in SIAM J. Financial Mathematics.

On the set of robust sustainable thresholds (with P. Gajardo and C. Hermosilla). Natural Resources Modeling, Vol. 34 (4) (2021).

Stability results for second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations (with O. Bokanowski and C. Reisinger). Numerische Mathematik, Vol. 148 (1), pp. 187-222 (2022).

A Level-Set Approach for Stochastic Optimal Control Problems under Controlled-Loss Constraints (with G. Bouveret), J. of Optimization Theory and Applications, Vol. 186 (3), pp. 779-805 (2020).

Optimal management of pumped hydroelectric production with state constrained optimal control (with T. Vargiolu), J. of Economic Dynamics and Control, Vol. 126 (2020).

Probabilistic error analysis for some approximation schemes to optimal control problems (with C. Reisinger), Systems & Control letters, Vol. 137 (2020).

Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems (with C. Reisinger), CAMWA: Computer and Mathematics with Applications, Vol. 79 (7), pp. 2099-2118 (2020).

Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains (with C. Reisinger and J. Rotaetxe), Journal of Differential Equations, Vol. 268 (12), pp. 7843-7876 (2020).

Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems (with E. R. Jakobsen and C. Reisinger), Electronic Communications in Probability, Vol. 24 (59), pp. 1-10 (2019).

Infinite horizon stochastic optimal control problems with running maximum cost (with A. Kroner and H. Zidani), SIAM J. Control and Optim. , Vol. 56 (5), pp. 3296–3319 (2018).

High-order filtered schemes for time-dependent second order HJB equations (with O. Bokanowski and C. Reisinger), ESAIM: M2AN, Vol. 54 (1), pp. 69-97 (2018).

State-constrained stochastic optimal control problems via reachability approach (with O. Bokanowski and H. Zidani), SIAM J. Control and Optim., Vol. 54 (5), pp. 2568-2593 (2016).

Zubov's method for controlled diffusions with state constraints (with L. Grune), Nonlinear Differential Equations and Applications, Vol. 22 (6), pp. 1765-1799 (2015).

Dynamic Programming and error estimates for stochastic control problems with maximum cost (with O. Bokanowski and H. Zidani), Appl. Math Optim., Vol. 71 (1), pp. 125--163 (2015).

A patchy dynamic programming scheme for a class of Hamilton-Jacobi-Bellman equations (with S. Cacace, E. Cristiani and M. Falcone), SIAM J. Scientific Computing, Vol. 34, No. 5, pp. A2625-A2649 (2012).

Publications in peer-reviewed proceedings and book chapters:

A Hamilton-Jacobi-Bellman approach for the numerical computation of probabilistic state constrained reachable sets (with M. Assellaou). In Falcone et al (Ed.), Numerical methods for Optimal Control problems. Springer INDAM Series (2019).

Boundary Mesh Refinement for Semi-Lagrangian Schemes (with C. Reisinger and J. Rotaetxe). In Kalise et al (Ed.), Hamilton-Jacobi-Bellman Equations. Numerical Methods and Applications in Optimal Control (pp. 167—188). Radon Series on Computational and Applied Mathematics, De Gruyter (2018).

Recent results in Hamilton-Jacobi-Bellman theory (with A. Festa, R. Guglielmi, C. Hermosilla, S. Sahu, A. Sassi, F. Silva). Book chapter in ``Optimal Control Design: Novel Directions and Applications''. Springer, Lecture notes in Mathematics. DOI: 10.1007/978-3-319-60771-9 (2017).