# Andrea Cosso

**Assistant Professor (RTDb)**

from November 2017 at the **University of Bologna**

*Department of Mathematics*

*Piazza di Porta S. Donato, 5*

*40126 Bologna, Italy*

* Office:* L5

* Phone:* +39 051 2094475

* e-mail:* andrea.cosso at unibo.it

**Research interests**

*Probability, stochastic control, stochastic analysis, mathematical finance.*

**Past positions**

**Assistant Professor (RTDa)**at**Politecnico di Milano**,**Post-doc**at**LPMA**(**L**aboratoire de**P**robabilités et**M**odèles**A**léatoires), Université Paris Diderot (Paris 7). January 2014 - December 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**

**BSDE representation and randomized dynamic programming principle for stochastic control problems of infinite-dimensional jump-diffusions**, (with Elena Bandini and Fulvia Confortola),*preprint*, [ArXiv].**Ergodic control of infinite dimensional SDEs with degenerate noise**, (with Giuseppina Guatteri and Gianmario Tessitore), to appear in*ESAIM: Control, Optimisation and Calculus of Variations*, [ArXiv].**The value of informational arbitrage**, (with Huy N. Chau and Claudio Fontana),*preprint*, [ArXiv], [SSRN].**Zero-sum stochastic differential games of generalized McKean-Vlasov type**, (with Huyên Pham),*preprint*, [ArXiv], [HAL].**Backward SDEs and infinite horizon stochastic optimal control**, (with Fulvia Confortola and Marco Fuhrman), to appear in*ESAIM: Control, Optimisation and Calculus of Variations*, [ArXiv].**Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem**, (with Elena Bandini, Marco Fuhrman, Huyên Pham), to appear in*Stochastic Processes and their Applications*, [ArXiv], [HAL].**Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics**, (with Erhan Bayraktar and Huyên Pham),*Transactions of the American Mathematical Society*, (2018), 370 (3), 2115-2160, [ArXiv], [HAL], [Article].**Backward SDEs for optimal control of partially observed path-dependent stochastic systems: a control randomization approach**, (with Elena Bandini, Marco Fuhrman, Huyên Pham),*The Annals of Applied Probability*,**Optimal investment with intermediate consumption under no unbounded profit with bounded risk**, (with Huy N. Chau, Claudio Fontana, Oleksii Mostovyi),*Journal of Applied Probability*, (2017), 54 (3), 710-719, [ArXiv], [Article].**BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data**, (with Huyên Pham and Hao Xing),*Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques*, (2017), 53 (4), 1528-1547, [ArXiv], [HAL], [Article].**Strong-viscosity solutions: semilinear parabolic PDEs and path-dependent PDEs**, (with Francesco Russo), to appear in*Osaka Journal of Mathematics*, [ArXiv], [HAL].**Functional It**ô 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),*The Annals of Probability*, (2018), 46 (1), 126-174, [ArXiv], [HAL], [Article].**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),*The Annals of Applied Probability*,**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 [Article], [SSRN].**Does an equity holding tax help to stabilize a VaR regulated financial market?**,*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**

*Zero-sum stochastic differential games of generalized McKean-Vlasov type.***Conference on "Stochastic modeling and financial applications"**,*Invited talk.**Randomization method in stochastic optimal control.***Workshop on BSDEs and SPDEs**,*Invited talk.**Randomization method in stochastic optimal control.***First Italian Meeting on Probability and Mathematical Statistics**,*Invited talk.**Randomization method in stochastic optimal control.***Young Researcher Workshop on Robust Mathematical Finance**,*Invited talk.**Randomization method in stochastic optimal control.*,**Seminar***Backward SDE representation for stochastic control problems with nondominated controlled intensity.***XVIII Workshop on Quantitative Finance**,*Contributed talk.**Robust feedback switching control.***Workshop on "Model Uncertainty & Robust Finance"**, Università di Milano, November 10-11, 2016.*Contributed talk.**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.*Contributed talk.**Randomization method and backward SDEs for optimal control of partially observed path-dependent stochastic systems.*, Università di Milano-Bicocca, February 10, 2016.**Seminar***Randomization method for optimal control of partially observed path-dependent SDEs.*, Università di Padova, October 21, 2015.**Seminar***Randomization method for optimal control of partially observed path-dependent SDEs.***Financial/Actuarial Mathematics**, Ann Arbor, Michigan, USA, October 14, 2015.*Seminar**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.*Invited talk.**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.*Invited talk.**Robust feedback switching control.***Paris-Southeast Asia Conference in Mathematical Finance**, Siem Reap, Cambodia, February 7-11, 2015.*Contributed talk.**Robust feedback switching control.***NUS-UParis Diderot Workshop on Quantitative Finance**, Singapore, February 3-5, 2015.*Contributed talk.**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.*Invited talk.**BSDE representation for stochastic control problems with controlled intensity.***Second Young researchers meeting on BSDEs, Numerics and Finance**, Bordeaux, July 7-9, 2014.*Contributed talk.**A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs.*, ENSTA, Paris, May 12, 2014.**Seminar***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”,**Un**i**versité Paris Diderot (Paris 7), January 30, 2014.*Strong-viscosity solutions to path-dependent PDEs. Work***shop on path-dependent SDEs, Pi**sa, January 21-22, 2014. Cont*ributed talk.**Feynman-Kac representation for Hamilton-Jacobi-Bellman(-Isaacs) equations. Semi*STA, Paris, October 28, 2013.**nar, EN***The path-dependent heat equation. Equa***dif Semi**litecnico di Milano, June 26, 2012.*nar, Po**Stochastic differential games involving impulse controls. Semi***nar Gro****upe de Travail “Fin**a**nce Mathématique, Probabilités Numériques et Statistique des Processus”,Unive**rsité Paris Diderot (Paris 7), October 25, 2012.*Stochastic differential games involving impulse controls. GNAMPA S***ummer School, Gaeta,**June 11-15, 2012. Contribu*ted talk.**Quasi-variational inequalities and backward stochastic differential equations. Stochast***ic Analysis Seminar,**cnico di Milano, September 27, 2011.*Polite**Does an equity holding tax help to stabilize a VaR regulated market? XII Work***shop on Quantitative Finance, Univer**s*i*tà di Padova, January 27-28, 2011. Contribu*ted talk.**Does an equity holding tax help to stabilize a VaR regulated market? Mathemat***ical Finance Seminar,**cnico di Milano, December 14, 2010.*Polite*