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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, IRMARUMR 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 110, 1981 pp. 162. Lecture Notes in Mathematics 972. SpringerVerlag, Berlin (1982), 
[2] 
Bismut, J.M.:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14, 419444(1976), 
[3] 
Buckdahn, R., Li, J., Peng, S.:Meanfield backward stochastic differential equations and related partial differential equations. Stoch. Process. Appl. 119, 31333154(2009), 
[4] 
Haussmann, U.G.:Optimal stationary control with state and control dependent noise. SIAM J. Control. 9, 184198(1971), 
[5] 
Kohlmann, M., Tang, S.:Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42, 11181142(2003), 
[6] 
Peng, S.:Stochastic HamiltonJacobiBellman equations. SIAM J. Control Optim. 30, 284304(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, 5375(2003), 
[8] 
Wonham, W.M.:On a matrix Riccati equation of stochastic control. SIAM J. Control. 6, 681697(1968), 
[9] 
Wu, H., Zhou, X.:Stochastic frequency characteristics. SIAM J. Control Optim. 40, 557576(2001), 
[10] 
Yong, J., Zhou, X.Y.:Stochastic Controls:Hamiltonian Systems and HJB Equations. SpringerVerlag, 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 110, 1981 pp. 162. Lecture Notes in Mathematics 972. SpringerVerlag, Berlin (1982), 
[2] 
Bismut, J.M.:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14, 419444(1976), 
[3] 
Buckdahn, R., Li, J., Peng, S.:Meanfield backward stochastic differential equations and related partial differential equations. Stoch. Process. Appl. 119, 31333154(2009), 
[4] 
Haussmann, U.G.:Optimal stationary control with state and control dependent noise. SIAM J. Control. 9, 184198(1971), 
[5] 
Kohlmann, M., Tang, S.:Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42, 11181142(2003), 
[6] 
Peng, S.:Stochastic HamiltonJacobiBellman equations. SIAM J. Control Optim. 30, 284304(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, 5375(2003), 
[8] 
Wonham, W.M.:On a matrix Riccati equation of stochastic control. SIAM J. Control. 6, 681697(1968), 
[9] 
Wu, H., Zhou, X.:Stochastic frequency characteristics. SIAM J. Control Optim. 40, 557576(2001), 
[10] 
Yong, J., Zhou, X.Y.:Stochastic Controls:Hamiltonian Systems and HJB Equations. SpringerVerlag, New York (1999), 
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