# IRMARÉquipe de Processus Stochastiques

### Université de Rennes 1Campus de Beaulieu35042 Rennes Cedex, France

Bâtiment: 22Bureau: 314Téléphone: 02 23 23 58 20Fax: 02 23 23 67 90E-mail: ying.hu@univ-rennes1.fr

## Thèmes de recherche

• Probabilités et processus stochastiques

• Equations différentielles stochastiques et équations différentielles stochastiques rétrogrades

• Controle et optimisation

• Mathématiques financières

• Méthodes probabilistes pour les EDP

• Théorie du potentiel

## Publications récentes

M. Fuhrman and Y. Hu, Infinite horizon BSDEs in infinite dimensions with continuous driver and applications. J. Evol. Equ. 6 (2006), 459-484.

P. Briand and Y. Hu, BSDE with quadratic growth and unbounded terminal value. Probab. Theory Related Fields 136 (2006), 604-618.
M. Fuhrman, Y. Hu and G. Tessitore, On a class of stochastic optimal control problems related to BSDEs with quadratic growth. SIAM J. Control Optim. 45 (2006), 1279-1296.
B. Delyon and Y. Hu, Simulation of conditioned diffusion and application to parameter estimation. Stochastic Process. Appl. 116 (2006), 1660-1675.
Y. Hu and S. Peng, On the comparison theorem of multidimensional BSDEs. C. R. Math. Acad. Sci. Paris 343  (2006), 135-140.
M. Fuhrman and Y. Hu, Backward stochastic differential equations in infinite dimensions with continuous driver and applications. Appl. Math. Optim. 56 (2007), 265-302.
Y. Hu and G. Tessitore, BSDE on an infinite horizon and elliptic PDEs in infinite dimension. NoDEA Nonlinear Differential Equations Appl. 14 (2007), 825-846.
M. Fuhrman, Y. Hu and G. Tessitore,  Stochastic control and BSDEs with quadratic growth. Control theory and related topics, 80-86, World Sci. Publ., Hackensack, NJ, 2007.

P. Briand and Y. Hu, Quadratic BSDEs with convex generators and unbounded terminal conditions. Probab. Theory Related Fields 141 (2008), 543-567.
Y. Hu, J. Ma, S. Peng and S. Yao, Representation theorems for quadratic ${\cal F}$-consistent nonlinear expectations. Stochastic Process. Appl. 118 (2008), 1518-1551.
M. Fuhrman, Y. Hu and G. Tessitore, Ergodic BSDEs and optimal ergodic control in Banach spaces. SIAM J. Control Optim. 48 (2009), 1542-1566.
Y. Hu and S. Tang, Multi-dimensional BSDE with oblique reflection and optimal switching. Probab. Theory Related Fields. 147 (2010), 89-121.
R. Buckdahn and Y. Hu, Probabilistic interpretation of a coupled system of Hamilton-Jacobi-Bellman equations. J. Evol. Equ. 10  (2010),  529-549.
X. Bao, F. Delbaen and Y. Hu, Existence and Non-uniqueness of Solutions for BSDE. Contemporary quantitative finance, 123-134, Springer, Berlin, 2010.

F. Delbaen, Y. Hu and X. Bao, Backward SDEs with superquadratic growth. Probab. Theory Related Fields. 150 (2011), 145-192.
F. Delbaen, Y. Hu and A. Richou, On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011), 559–574,
A. Debussche, Y. Hu and G. Tessitore, Ergodic BSDEs under weak dissipative assumptions. Stochastic Process. Appl. 121 (2011), 407–426.
P. Cheridito and Y. Hu, Optimal consumption and investment in incomplete markets with general constraints. Stoch. Dyn. 11 (2011), 283-299.
Y. Hu and M. Schweizer, Some new BSDE results for an infinite-horizon stochastic control problem. Advanced mathematical methods for finance, 367-395, Springer, Berlin, 2011.

R. Buckdahn, Y. Hu and J. Li,
Stochastic representation for solutions of Isaacs' type integral-partial differential equations. Stochastic Process. Appl. 121 (2011), 2715-2750.

Y. Hu, H. Jin and X. Y. Zhou, Time-inconsistent stochastic linear--quadratic control.  SIAM J. Control Optim.  50 (2012), 1548-1572.

M. Fuhrman, Y. Hu and G. Tessitore, Stochastic maximum principle for optimal control of SPDEs. C. R. Math. Acad. Sci. Paris 350 (2012), 683–688.

M. Fuhrman, Y. Hu and G. Tessitore, Stochastic maximum principle for optimal control of SPDEs. Appl. Math. Optim. To appear.  arXiv:1302.0286, 2013.
S. Cohen and Y. Hu, Ergodic BSDEs driven by Markov chains. SIAM J. Control Optim. To appear.  arXiv:1207.5680, 2012.

Y. Hu and S. Tang, Switching games of backward stochastic differential equations. arXiv:0806.2058, 2008.
Y. Hu and S. Peng,
Some estimates for martingale representation under G-expectation. arXiv:1004.1098,  2010.
U. Horst, Y. Hu, P. Imkeller, A. Réveillac and J. Zhang, Forward-backward systems for expected utility maximization. arXiv:1110.2713, 2011.

Y. Hu and Z. Qian, BMO martingales and positive solutions of heat equations. arXiv:1201.5454, 2012.

Y. Hu, Z. Qian and Z. Zhang, Gradient estimates for porous medium and fast diffusion equations via FBSDE approach. arXiv:1206.1394, 2012.

F. Delbaen, Y. Hu and A. Richou, On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case.  arXiv:1303.4859, 2013.