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Piecewise constant martingales and lazy clocks
Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs
1. Univ Rennes, CNRS, IRMAR-UMR 6625, 35000 Rennes, France; |
2. Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433 China |
References:
[1] |
Bensoussan, A.:Lectures on stochastic control. In:Mitter, S.K., Moro, A. (eds.) Nonlinear filtering and stochastic control, Proceedings of the 3rd 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Cortona, July 1-10, 1981 pp. 1-62. Lecture Notes in Mathematics 972. Springer-Verlag, Berlin (1982), |
[2] |
Bismut, J.M.:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14, 419-444(1976), |
[3] |
Buckdahn, R., Li, J., Peng, S.:Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Process. Appl. 119, 3133-3154(2009), |
[4] |
Haussmann, U.G.:Optimal stationary control with state and control dependent noise. SIAM J. Control. 9, 184-198(1971), |
[5] |
Kohlmann, M., Tang, S.:Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42, 1118-1142(2003), |
[6] |
Peng, S.:Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 30, 284-304(1992), |
[7] |
Tang, S.:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42, 53-75(2003), |
[8] |
Wonham, W.M.:On a matrix Riccati equation of stochastic control. SIAM J. Control. 6, 681-697(1968), |
[9] |
Wu, H., Zhou, X.:Stochastic frequency characteristics. SIAM J. Control Optim. 40, 557-576(2001), |
[10] |
Yong, J., Zhou, X.Y.:Stochastic Controls:Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999), |
show all references
References:
[1] |
Bensoussan, A.:Lectures on stochastic control. In:Mitter, S.K., Moro, A. (eds.) Nonlinear filtering and stochastic control, Proceedings of the 3rd 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Cortona, July 1-10, 1981 pp. 1-62. Lecture Notes in Mathematics 972. Springer-Verlag, Berlin (1982), |
[2] |
Bismut, J.M.:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14, 419-444(1976), |
[3] |
Buckdahn, R., Li, J., Peng, S.:Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Process. Appl. 119, 3133-3154(2009), |
[4] |
Haussmann, U.G.:Optimal stationary control with state and control dependent noise. SIAM J. Control. 9, 184-198(1971), |
[5] |
Kohlmann, M., Tang, S.:Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42, 1118-1142(2003), |
[6] |
Peng, S.:Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 30, 284-304(1992), |
[7] |
Tang, S.:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42, 53-75(2003), |
[8] |
Wonham, W.M.:On a matrix Riccati equation of stochastic control. SIAM J. Control. 6, 681-697(1968), |
[9] |
Wu, H., Zhou, X.:Stochastic frequency characteristics. SIAM J. Control Optim. 40, 557-576(2001), |
[10] |
Yong, J., Zhou, X.Y.:Stochastic Controls:Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999), |
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