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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 30 open journal systems 


A General Stochastic Maximum Principle for Singular Control Problems

Seid Bahlali, University Med Khider, Algeria
Brahim Mezerdi, University Med Khider, Algeria


Abstract
We consider the stochastic control problem in which the control domain need not be convex, the control variable has two components, the first being absolutely continuous and the second singular. The coefficients of the state equation are non linear and depend explicitly on the absolutely continuous component of the control. We establish a maximum principle, by using a spike variation on the absolutely continuous part of the control and a convex perturbation on the singular one. This result is a generalization of Peng's maximum principle to singular control problems.


Full text: PDF

Pages: 988-1004

Published on: July 21, 2005


Bibliography

 

[1] Bahlali, Seid; Chala, Adel. The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients. Random Oper. Stochastic Equations 13 (2005), no. 1, 1--10. MR2130243

 

[2] Bahlali, S.; Djehiche, B.; Mezerdi, B. The relaxed maximum principle in singular control of diffusions, Submitted to SIAM J. Control and Optim. (2005)

 

[3] Bensoussan, A. Lectures on stochastic control. Nonlinear filtering and stochastic control (Cortona, 1981), 1--62, Lecture Notes in Math., 972, Springer, Berlin-New York, 1982. MR0705931 (84h:93076)

 

[4] Benev s, V. E.; Shepp, L. A.; Witsenhausen, H. S. Some solvable stochastic control problems. Stochastics 4, no. 1, 39--83. (1980/81), MR0587428 (81m:93084)

 

[5] Cadenillas, Abel; Haussmann, Ulrich G. The stochastic maximum principle for a singular control problem. Stochastics Stochastics Rep. 49 (1994), no. 3-4, 211--237. MR1785006 (2001e:49048)

 

[6] Chow, Pao Liu; Menaldi, José-Luis; Robin, Maurice. Additive control of stochastic linear systems with finite horizon. SIAM J. Control Optim. 23 (1985), no. 6, 858--899. MR0809540 (87b:49040)

 

[7] Davis, M. H. A.; Norman, A. R. Portfolio selection with transaction costs. Math. Oper. Res. 15 (1990), no. 4, 676--713. MR1080472 (92b:90036)

 

[8] Haussmann, Ulrich G.; Suo, Wulin. Singular optimal stochastic controls. I. Existence. SIAM J. Control Optim. 33 (1995), no. 3, 916--936. MR1327243 (96e:93071)

 

[9] Haussmann, Ulrich G.; Suo, Wulin. Singular optimal stochastic controls. II. Dynamic programming. SIAM J. Control Optim. 33 (1995), no. 3, 937--959. MR1327244 (96e:93072)

 

[10] Haussmann, Ulrich G.; Suo, Wulin. Existence of singular optimal control laws for stochastic differential equations. Stochastics Stochastics Rep. 48 (1994), no. 3-4, 249--272. MR1782750 (2001e:49035)

 

[11] Karatzas, Ioannis; Shreve, Steven E. Connections between optimal stopping and singular stochastic control. I. Monotone follower problems. SIAM J. Control Optim. 22 (1984), no. 6, 856--877. MR0762624 (87h:93075a)

 

[12] Peng, Shi Ge. A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28 (1990), no. 4, 966--979. MR1051633 (91g:49013)

 

 

 

 

 

















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Electronic Journal of Probability. ISSN: 1083-6489