On a class of stochastic optimal control problems related to bsdes with quadratic growth

SIAM Journal on Control and Optimization

Volumn 45, Issue 4, 2006, Pages 1279-1296

  Fuhrman, Marco ^a   Hu, Ying ^b   Tessitore, Gianmario ^c  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITÉ DE RENNES 1   (France)

^c UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Backward stochastic differential equations; Quadratically growing driver; Stochastic optimal control; Unbounded final condition

Indexed keywords

COST FUNCTIONS; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; PROBLEM SOLVING; SET THEORY; STOCHASTIC CONTROL SYSTEMS;

CONTROL PROCESS; INITIAL VALUE; LINEAR GROWTH; QUADRATIC GROWTH;

OPTIMAL CONTROL SYSTEMS;

EID: 34547211757     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/050633548     Document Type: Article

References (12)

1. J.-P. AUBIN AND H. FRANKOWSKA, Set-Valued Analysis, Systems Control Found. Appl. 2, Birkhäuser Boston, Boston, MA, 1990.
2. P. BRIAND AND Y. HU, BSDE with quadratic growth and unbounded terminal value, Probab. Theory Related Fields, to appear.
3. C. DELLACHERIE AND P. A. MEYER, Probabilities and Potential, North-Holland, Amsterdam, 1978.
4. N. EL KAROUI, S. PENG, AND M. C. QUENEZ, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), pp. 1-71.
5. N. EL KAROUI AND S. HAMADENE, BSDEs and risk-sensitive control, zero-sum and nonzerosum game problems of stochastic functional differential equations, Stochastic Process. Appl., 107 (2003), pp. 145-169.
6. M. FUHRMAN, A class of stochastic optimal control problems in Hubert spaces: BSDEs and optimal control laws, state constraints, conditioned processes, Stochastic Process. Appl., 108 (2003), pp. 263-298.
7. M. FUHRMAN AND G. TESSITORE, Existence of optimal stochastic controls and global solutions of forward-backward stochastic differential equations, SIAM J. Control Optim., 43 (2004), pp. 813-830.
8. F. GOZZI, Global regular solutions of second order Hamilton-Jacobi equations in Hilbert spaces with locally Lipschitz nonlinearities, J. Math. Anal. Appl., 198 (1996), pp. 399-443.
9. S. HAMADÈNE AND J.-P. LEPELTIER, Backward equations, stochastic control and zero-sum stochastic differential games, Stochastics Stochastics Rep., 54 (1995), pp. 221-231.
10. M. KOBYLANSKI, Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab., 28 (2000), pp. 558-602.
11. E. PARDOUX AND S. PENG, Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14 (1990), pp. 55-61.
12. J. YONG AND X. Y. ZHOU, Stochastic Controls. Hamiltonian Systems and HJB Equations, Springer, New York, 1999.