Research

Research interests

Stochastic filtering, optimal control problems under full and partial observation, and their applications to economics and finance.

Hamilton-Jacobi-Bellman equations, Backward Stochastic Differential Equations and their applications.

Stochastic processes with discontinuous trajectories, random measures and their applications.

Risk measures, g-expectations and robustness.

Publications & accepted papers

• A. Calvia, F. Gozzi, F. Lippi, G. Zanco, A simple planning problem for COVID-19 lockdown: a dynamic programming approach, Econ. Theory, 77:1-2 (2024), pp. 169–196, D.O.I., Open Access.

• A. Calvia, G. Cappa, F. Gozzi, E. Priola, HJB equations and stochastic control on half-spaces of Hilbert spaces, J. Optim. Theory Appl., 198 (2023), pp. 710-744, D.O.I., Open Access.

• E. Bandini, A. Calvia, K. Colaneri, Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics, Stoch. Proc. Appl., 151 (2022), pp. 396–435, D.O.I.
  Preprint version, arXiv:2004.12944.

• A. Calvia, G. Ferrari, Nonlinear filtering of partially observed systems arising in singular stochastic optimal control. Appl. Math. Optim., 85:25 (2022), D.O.I., Open Access.

• A. Calvia, S. Federico, F. Gozzi, State constrained control problems in Banach lattices and applications, SIAM J. Control Optim., 59 (2021), pp. 4481–4510,  D.O.I.
  Preprint version, arXiv:2009.11268.  

• A. Calvia, E. Rosazza Gianin, Risk measures and progressive enlargement of filtration: a BSDE approach, SIAM J. Financial Math., 11 (2020), pp. 815-848, D.O.I.
  Preprint version, arXiv:1904.13257.

• A. Calvia, Stochastic filtering and optimal control of pure jump Markov processes with noise-free partial observation, ESAIM: COCV, 26 (2020) 25, D.O.I.
  Preprint version, arXiv:1803.0692.

• A. Calvia, Optimal control of continuous-time Markov chains with noise-free observation, SIAM J. Control Optim., 56 (2018), pp. 2000–2035, D.O.I.
  Preprint version, arXiv:1707.07202.

Preprints

• A. Calvia, S. Federico, G. Ferrari, F. Gozzi, A mean-field model of optimal investment, arXiv:2404.02871.

• A. Calvia, F. Gozzi, M. Leocata, G. I. Papayiannis, A. Xepapadeas, A. N. Yannacopoulos, An optimal control problem with state constraints in a spatio-temporal economic growth model on networks, arXiv:2304.11568.

Ongoing projects

• Optimal control of Piecewise Deterministic Markov Processes of McKean-Vlasov type, with Dr. Elena Bandini.

• Stochastic filtering and singular control under full or partial information, with Prof. Giorgio Ferrari.

• Optimal retail energy pricing, with Prof. René Aïd and Prof. Salvatore Federico.

• Partial smoothing and applications to optimal control problems, with Prof. Fausto Gozzi, Prof. Federica Masiero, and Prof. Gianmario Tessitore.

• Optimal control with unobserved parameters, with Prof. Marco Fuhrman.

• Optimal control of measure-valued Piecewise Deterministic Markov Processes and applications, with Prof. Fulvia Confortola, Prof. Andrea Cosso, and Dr. Mattia Martini.

PhD Thesis

Optimal control of pure jump Markov processes with noise-free partial observation.

University of Milano-Bicocca, Dep. of Mathematics and its Applications.

PhD Program in Pure and Applied Mathematics. Thesis defended on 22 February 2018.