Existence of optimal stochastic controls and global solutions of forward-backward stochastic differential equations

SIAM Journal on Control and Optimization

Volumn 43, Issue 3, 2005, Pages 813-830

  Fuhrman, Marco ^a   Tessitore, Gianmario ^b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

Forward backward stochastic differential equations; Stochastic optimal control

Indexed keywords

DIFFERENCE EQUATIONS; FEEDBACK CONTROL; INTEGRATION; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

CONTROL-THEORETIC INTERPRETATIONS; DIFFUSION COEFFICIENTS; FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC OPTIMAL CONTROL;

STOCHASTIC CONTROL SYSTEMS;

EID: 19944417285     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903428664     Document Type: Article

References (23)

1. F. ANTONELLI, Backward-forward stochastic differential equations, Ann. Appl. Probab., 3 (1993), pp. 777-793.
2. V. BALLY, E. PARDOUX, AND L. STOICA, Backward Stochastic Differential Equations Associated to a Symmetric Markov Process, Tech. rep. 4454, INRIA Rocquencourt, Le Chesnay, France, 2002.
3. S. CERRAI, Second Order PDE's in Finite and Infinite Dimensions. A Probabilistic Approach, Lecture Notes in Math. 1762, Springer-Verlag, Berlin, 2001.
4. F. DELARUE, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stochastic Process. Appl., 99 (2002), pp. 209-286.
5. N. EL KAROUI, D. HU NGUYEN, AND M. JEANBLANC-PIQUÉ, Compactification methods in the control of degenerate diffusion: Existence of an optimal control, Stochastics, 20 (1987), pp. 169-219.
6. N. EL KAROUI, S. PENG, AND M. C. QUENEZ, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), pp. 1-71.
7. W. H. FLEMING AND H. M. SONER, Controlled Markov Processes and Viscosity Solutions, Appl. Math. 25, Springer-Verlag, New York, 1993.
8. U. G. HAUSSMANN AND W. SUO, Existence of singular optimal control laws for stochastic differential equations, Stochastics Stochastics Rep., 48 (1994), pp. 249-272.
9. S. HAMADÈNE, Backward forward SDE's and stochastic differential games, Stochastic Process. Appl., 77 (1998), pp. 1-15.
10. S. HAMADÈNE AND J.-P. LEPELTIER, Zero sum differential games and backward equations, Systems Control Lett., 24 (1995), pp. 259-263.
11. S. HAMADÈNE, J.-P. LEPELTIER, AND S. PENG, BSDEs with continuous coefficients and stochastic differential games, in Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser. 364, N. El Karoui, L. Mazliak, eds., Longman, Harlow, UK, 1997, pp. 115-128.
12. U. G. HAUSSMANN AND J.-P. LEPELTIER, On the existence of optimal controls, SIAM J. Control Optim., 28 (1990), pp. 851-902.
13. Y. HU AND S. PENG, Solution of forward-backward stochastic differential equations, Probab. Theory Related Fields, 103 (1995), pp. 273-283.
14. Y. HU AND J. YONG, Forward-backward stochastic differential equations with nonsmooth coefficients, Stochastic Process. Appl., 87 (2000), pp. 93-106.
15. O. A. LADYZENSKAJA, V. A. SOLONNIKOV, AND N. N. URAL'CEVA, Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monogr. 23, AMS, Providence, RI, 1968.
16. J. MA, P. PROTTER, AND J. YONG, Solving forward-backward stochastic differential equations explicitly - a four step scheme, Probab. Theory Related Fields, 98 (1994), pp. 339-359.
17. J. MA AND J. YONG, Forward-Backward Stochastic Differential Equations and Their Applications, Lecture Notes in Math. 1702, Springer-Verlag, Berlin, 1999.
18. E. PARDOUX, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, in Stochastic Analysis and Related Topics, the Geilo Workshop 1996, Progr. Probab. 42, L. Decreusefond, J. Gjerde, B. Øksendal, and A. S. Üstünel, eds., Birkhäuser Boston, Boston, 1998, pp. 79-127.
19. E. PARDOUX, BSDE's, weak convergence and homogeneization of semilinear PDE's, in Nonlinear Analysis, Differential Equations and Control, F. H. Clarke and R. J. Stern, eds., Kluwer, Dordrecht, The Netherlands, 1999, pp. 503-549.
20. E. PARDOUX AND S. TANG, Forward-backward stochastic differential equations and quasilinear PDEs, Probab. Theory Related Fields, 114 (1999), pp. 123-150.
21. S. PENG AND Z. WU, Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., 37 (1999), pp. 825-843.
22. M. SHARPE, General Theory of Markov Processes, Pure Appl. Math. 133, Academic Press, Boston, 1988.
23. J. YONG AND X. Y. ZHOU, Stochastic Controls, Appl. Math. 43, Springer-Verlag, New York, 1999.