The stochastic maximum principle in optimal control of degenerate diffusions with non-smooth coefficients

Random Operators and Stochastic Equations

Volumn 17, Issue 1, 2009, Pages 37-54

  Chighoub, Farid ^a   Djehiche, Boualem ^b   Mezerdi, Brahim ^a  

^a UNIVERSITY OF BISKRA   (Algeria)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Maximum principle; Non smooth coefficients; Optimal control; Stochastic differential equation

Indexed keywords

EID: 84858390664     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/ROSE.2009.002     Document Type: Article

References (20)

1. K. Bahlali, B. Djehiche and B. Mezerdi, On the Stochastic Maximum Principle in Optimal Control of Degenerate Diffusions with Lipschitz Coefficients, Appl. Math. Optim. 56 (2007), pp. 364-378. (Pubitemid 350205913)
2. K. Bahlali, B. Mezerdi and Y. Ouknine, The maximum principle in optimal control of a diffusions with nonsmooth coefficients, Stoch. Stoch. Rep. 57 (1996), pp. 303-316.
3. A. Bensoussan, Lectures on stochastic control, Lect. Notes in Math. 972, Springer, Berlin, 1983.
4. J. M. Bismut, An introductory approach to duality in optimal stochastic control, SIAM Rev. 20(1) (1978), pp. 62-78.
5. N. Bouleau and F. Hirsch, On the derivability with respect to the initial data of the solution of a stochastic differential equation with Lipschitz coefficients, Lect. Notes in Math. 1393, pp. 39-57, Springer, Berlin, 1989.
6. N. Bouleau and F. Hirsch, Sur la propriété du flot d'une équation différentielle stochastique, C. R. Acad. Sci. Paris 306 (1988), pp. 421-424.
7. A. Cadenillas and I. Karatzas, The stochastic maximum principle for linear convex optimal control with random coefficients, SIAM J. Control Optim. 33(2) (1995), pp. 590-624.
8. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
9. I. Ekeland, Non convex minimization problems, Bull. Am. Math. Soc. (N. S.) 1 (1979), pp. 443-474.
10. R. J. Elliott and M. Kohlmann, The variational principle and stochastic optimal control, Stochastics 3 (1980), pp. 229-241.
11. R. J. Frankowska, The first order necessary conditions for nonsmooth variational and control problems, SIAM J. Control Optim. 22(1) (1984), pp. 1-12.
12. U. G. Haussmann, A stochastic maximum principle for optimale control of diffusions, Longman Scientific & Technical, Harlow. Pitman Research Notes in Mathematics Series 151, Wiley, New York, 1986.
13. N. V. Krylov, Controlled Diffusion Processes, Springer, Berlin, 1980.
14. N. J. Kushner, Necessary conditions for continuous parameter stochastic optimization problems, SIAM J. Control Optim. 10 (1972), pp. 550-565.
15. B. Mezerdi, Necessary conditions for optimality for a diffusion with a non smooth drift, Stochastics 24 (1988), pp. 305-326.
16. S. Peng, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim. 28 (1990), pp. 966-979. (Pubitemid 20720202)
17. R. T. Rockafellar, Conjugat convex functions in optimal control problems and the calculus of variations, J. Math. Anal. Appl. 32 (1970), pp. 174-222.
18. J. Warga, Necessary conditions without differentiability assumptions in optimal control. J. Differ. Equ. 18 (1975), pp. 41-62.
19. B. Yang, Necessary conditions for optimal controls of forward backward stochastic systems with non smooth cost functionals J. Fudan Univ. Nat. Sci. 39(1) (2000), pp. 61-67.
20. X. Y. Zhou, Stochastic near optimal controls: necessary and sufficient conditions for near optimality, SIAM J. Control Optim. 36(3) (1998), pp. 929-947. (Pubitemid 128493580)