Andrea Cosso



Assistant Professor

from January 2016 at Politecnico di Milano
Dipartimento di Matematica
Via Bonardi 9, 20133 Milano, Italy


Office: 526

Phone+39 02 2399 4614

Fax+39 02 2399 4626

e-mail: andrea.cosso at polimi.it




Research interests
Stochastic control, mathematical finance, stochastic analysis.



Past position
  • Post-doc at LPMA (Laboratoire de Probabilités et Modèles Aléatoires), Université Paris Diderot (Paris 7). January 1, 2014 - December 31, 2015.


Education
  • Ph.D. in Mathematical Models and Methods in Engineering, Politecnico di Milano, January 1, 2011 - December 31, 2013. Final examination and grade: February 20, 2014, cum laude.
    • Thesis
    • Title: Probabilistic representation of some classes of nonlinear PDEs and connections with stochastic optimal  control and stochastic analysis.
    • Advisor: Prof. Marco Fuhrman.
  • Master of Science in Mathematical Engineering, Politecnico di Milano, September 2008 - July 21, 2010. Final grade: 110/110 cum laude.
    • Thesis
    • Title: The effect of Value-at-Risk on endogenous risk.
    • Advisor: Prof. Emilio Barucci.
  • Graduate exchange program at Kungliga Tekniska Högskolan, January 2009 - June 2009.
  • Bachelor of Science in Mathematical Engineering, Politecnico di Milano, September 2005 - July 23, 2008. Final grade: 110/110 cum laude.
    • Thesis
    • Title: American options and variational inequalities.
    • Advisor: Prof. Sandro Salsa.



Preprints and publications

  • Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem, (with Elena Bandini, Marco Fuhrman, Huyên Pham), preprint, [ArXiv], [HAL].
  • Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics, (with Erhan Bayraktar and Huyên Pham), to appear in Transactions of the American Mathematical Society, [ArXiv], [HAL].
  • Randomization method and backward SDEs for optimal control of partially observed path-dependent stochastic systems, (with Elena Bandini, Marco Fuhrman, Huyên Pham), preprint, [ArXiv], [HAL].
  • Optimal investment with intermediate consumption under no unbounded profit with bounded risk, (with Huy N. Chau, Claudio Fontana, Oleksii Mostovyi)to appear in Journal of Applied Probability, [ArXiv].
  • BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data, (with Huyên Pham and Hao Xing)to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, [ArXiv], [HAL].
  • Strong-viscosity solutions: semilinear parabolic PDEs and path-dependent PDEs, (with Francesco Russo)preprint, [ArXiv], [HAL].
  • Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent Kolmogorov equations, (with Francesco Russo)Infinite Dimensional Analysis, Quantum Probability and Related Topics, (2016), 19 (4), 1-44, [ArXiv], [HAL], [Article].
  • Path-dependent equations and viscosity solutions in infinite dimension, (with Salvatore Federico, Fausto Gozzi, Mauro Rosestolato, Nizar Touzi), to appear in Annals of Probability, [ArXiv], [HAL].
  • Ergodicity of robust switching control and nonlinear system of quasi variational inequalities, (with Erhan Bayraktar and Huyên Pham), SIAM Journal on Control and Optimization, (2017), 55 (3), 1915-1953, [ArXiv], [HAL], [Article].
  • Long time asymptotics for fully nonlinear Bellman equations: a Backward SDE approach, (with Marco Fuhrman and Huyên Pham), Stochastic Processes and their Applications, (2016), 126 (7), 1932–1973, [ArXiv], [HAL], [Article].
  • Robust feedback switching control: dynamic programming and viscosity solutions, (with Erhan Bayraktar and Huyên Pham), SIAM Journal on Control and Optimization, (2016), 54 (5), 2594-2628, [ArXiv], [HAL], [Article].
  • Backward SDE representation for stochastic control problems with nondominated controlled intensity, (with Sébastien Choukroun), Annals of Applied Probability, (2016), 26 (2), 1208-1259, [ArXiv], [HAL], [Article].
  • Reflected BSDEs with nonpositive jumps, and controller-and-stopper games, (with Sébastien Choukroun and Huyên Pham), Stochastic Processes and their Applications, (2015), 125 (2), 597-633, [ArXiv], [HAL], [Article].
  • Viscosity solutions of path-dependent PDEs and non-Markovian forward-backward stochastic equations, preprint, [ArXiv].
  • American option valuation in a stochastic volatility model with transaction costs, (with Carlo Sgarra and Daniele Marazzina), Stochastics: An International Journal of Probability and Stochastic Processes, (2015), 87 (3), 518-536 [Article].
  • Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities, SIAM Journal on Control and Optimization, (2013), 51 (3), 2102-2131, [ArXiv], [Article].
  • Portfolio choices and VaR constraint with a defaultable asset, (with Emilio Barucci), Quantitative Finance, (2015), 15 (5), 853-864 [SSRN], [Article].
  • Does an equity holding tax help to stabilize a VaR regulated financial market?, (with Emilio Barucci), preprint, [SSRN].



Conference publications

  • Functional and Banach space stochastic calculi: Path-dependent Kolmogorov equations associated with the frame of a Brownian motion, (with Francesco Russo)Springer Proceedings in Mathematics and Statistics, (2016), 138, 27-80; Conference on "Stochastics for Environmental and Financial Economics" (SEFE 2015), Oslo, Norway, [Article].
  • Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations, (with Cristina Di Girolami and Francesco Russo)Contemporary Mathematics (AMS), (2016), 668, 43-65; Conference on "Probability on Algebraic and Geometric Structures", June 5-7, 2014, Carbondale, Illinois, USA, [ArXiv], [HAL], [Article].


Talks

  • Randomization method in stochastic optimal control. Workshop on BSDEs and SPDEs, University of Edinburgh, July 3-7, 2017.
  • Randomization method in stochastic optimal control. First Italian Meeting on Probability and Mathematical Statistics, Università di Torino - Politecnico di Torino, June 19-22, 2017.
  • Randomization method in stochastic optimal control. Young Researcher Workshop on Robust Mathematical Finance, ETH Zurich, April 26-28, 2017.
  • Randomization method in stochastic optimal control. Seminar, Università di Bologna, February 16, 2017.
  • Backward SDE representation for stochastic control problems with nondominated controlled intensity. XVIII Workshop on Quantitative Finance, Università di Milano-Bicocca, January 25-27, 2017.
    • Robust feedback switching controlWorkshop on "Model Uncertainty & Robust Finance", Università di Milano, November 10-11, 2016.
    • Functional versus Banach space stochastic calculus, and strong-viscosity solutions to path-dependent PDEs. Workshop on "Pathwise methods, Functional Calculus and applications in Mathematical Finance", Wolfgang Pauli Institute (WPI) Vienna, April 4-6, 2016.
    • Randomization method and backward SDEs for optimal control of partially observed path-dependent stochastic systems. Seminar, Università di Milano-Bicocca, February 10, 2016.
    • Randomization method for optimal control of partially observed path-dependent SDEs. Seminar, Università di Padova, October 21, 2015.
    • Randomization method for optimal control of partially observed path-dependent SDEs. Financial/Actuarial Mathematics Seminar, Ann Arbor, Michigan, USA, October 14, 2015.
    • Functional versus Banach space stochastic calculus and strong-viscosity solutions to semilinear parabolic path-dependent PDEs. 7th General AMaMeF and Swissquote Conference, Lausanne, Switzerland, September 7-11, 2015.
    • Functional versus Banach space stochastic calculus and strong-viscosity solutions to semilinear parabolic PDEs and path-dependent PDEs. 13th Viennese Workshop on Optimal Control and Dynamic Games, Vienna, Austria, May 15, 2015.
    • Robust feedback switching control. Paris-Southeast Asia Conference in Mathematical Finance, Siem Reap, Cambodia, February 7-11, 2015.
    • Robust feedback switching control. NUS-UParis Diderot Workshop on Quantitative Finance, Singapore, February 3-5, 2015.
    • Viscosity solutions for path-dependent PDEs in infinite dimension. Workshop on path-dependent PDEs and stochastic equations with memory, Università di Milano, January 23, 2015.
    • BSDE representation for stochastic control problems with controlled intensity. Second Young researchers meeting on BSDEs, Numerics and Finance, Bordeaux, July 7-9, 2014.
    • A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs. ENSTA/UMA Seminar, Paris, May 12, 2014.
    • Stochastic differential games involving impulse controls. Seminar Université de Bretagne Occidentale, Brest, March 4, 2014.
    • A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs. Seminar Groupe de Travail Finance Mathématique, Probabilités Numériques et Statistique des Processus”, Université Paris Diderot (Paris 7), January 30, 2014.

    • Strong-viscosity solutions to path-dependent PDEs. Workshop on path-dependent SDEs, Pisa, January 21-22, 2014.
    • Feynman-Kac representation for Hamilton-Jacobi-Bellman(-Isaacs) equations. ENSTA/UMA Seminar, Paris, October 28, 2013.
    • The path-dependent heat equation. Equadif Seminar, Politecnico di Milano, June 26, 2012.
    • Stochastic differential games involving impulse controls. Seminar Groupe de Travail Finance Mathématique, Probabilités Numériques et Statistique des Processus”, Université Paris Diderot (Paris 7), October 25, 2012.

    • Stochastic differential games involving impulse controls. GNAMPA Summer School, Gaeta, June 11-15, 2012.
    • Quasi-variational inequalities and backward stochastic differential equations. Stochastic Analysis Seminar, Politecnico di Milano, September 27, 2011.
    • Does an equity holding tax help to stabilize a VaR regulated market? XII Workshop on Quantitative Finance, Università di Padova, January 27-28, 2011.
    • Does an equity holding tax help to stabilize a VaR regulated market? Mathematical Finance Seminar, Politecnico di Milano, December 14, 2010.