References
- Alvarez , L. 2001 . Singular stochastic control, linear diffusions and optimal stopping: A class of solvable problems . SIAM J. Control Optim. , 39 ( 6 ) : 427 – 444 .
- Bahlali , S. and Chala , A. 2005 . The stochastic maximum principle in optimal control of singular diffusions with nonlinear coefficients . Random Oper. Stochastic Equations , 13 : 1 – 10 .
- Bahlali , S. and Mezerdi , B. 2005 . A general stochastic maximum principle for singular control problems . Electron. J. Probab. , 10 : 988 – 1004 .
- Baldursson , F.M. and Karatzas , I. 1997 . Irreversible investment and industry equilibrium . Finance Stoch. , 1 : 69 – 89 .
- Bather , J.A. and Chernoff , H. 1967 . Sequential decision in the control of a spaceship, (finite fuel) . J. Appl. Probab. , 49 : 584 – 604 .
- Bahlali , S. , Djehiche , B. and Mezerdi , B. 2007 . The relaxed maximum principle in singular control of diffusions . SIAM J. Control Optim. , 46 : 427 – 444 .
- Bahlali , K. , Chighoub , F. , Djehiche , B. and Mezerdi , B. 2009 . Optimality necessary conditions in singular stochastic control problems with non smooth data . J. Math. Anal. Appl. , 355 : 479 – 494 .
- Benĕs , V.E. , Shepp , L.A. and Witsenhausen , H.S. 1980 . Some solvable stochastic control problems . Stoch. Stoch. Rep. , 4 : 39 – 83 .
- Cadenillas , A. and Haussmann , U.G. 1994 . The stochastic maximum principle for a singular control problem . Stoch. Stoch. Rep. , 49 : 211 – 237 .
- Chaleyat-Maurel , M. , El Karoui , N. and Marchal , B. 1980 . Réflexion discontinue et systèmes stoshastiques . Ann. Probab. , 8 : 1049 – 1067 .
- Chow , P.L. , Menaldi , J.L. and Robin , M. 1985 . Additive control of stochastic linear systems with finite horizon . SIAM J. Control Optim. , 23 : 858 – 899 .
- Davis , M.H.A. and Norman , A. 1990 . Portfolio selection with transaction costs . Math. Oper. Res. , 15 : 676 – 713 .
- Dufour , F. and Miller , B. 2007 . Necessary conditions for optimality in singular control problems . Stochastics , 79 ( 5 ) : 469 – 504 .
- El Karoui , N. and Karatzas , I. 1988 . Probabilistic aspects of finite fuel, reflected follower problems . Acta Appl. Math. , 11 ( 3 ) : 223 – 258 .
- Elsanosi , I. , Øksendal , B. and Sulem , A. 2000 . Some solvable stochastic control problems with delay . Stoch. Stoch. Rep. , 71 : 69 – 89 .
- Fleming , W.H. and Soner , H.M. 2006 . Controlled Markov Processes and Viscosity Solutions , 2nd ed. , New York : Springer Verlag .
- Framstad , N.C. , Øksendal , B. and Sulem , A. 2004 . Sufficient stochastic maximum principle for optimal control of jumps diffusions and applications to finance . J. Optim. Theory Appl. , 121 : 77 – 98 . Errata: J. Optim. Theory and Appl. 124 (2) (2005), pp. 511–512
- Haussmann , U.G. and Suo , W. 1995 . Singular optimal stochastic controls I: Existence . SIAM J. Control Optim. , 33 : 916 – 936 .
- Haussmann , U.G. and Suo , W. 1995 . Singular optimal stochastic controls II: Dynamic programming . SIAM J. Control Optim. , 33 : 937 – 959 .
- Jeanblanc-Picqué , M. and Shiryaev , A.N. 1995 . Optimization of the flows of dividends . Russian Math. Surveys , 50 : 257 – 277 .
- Karatzas , I. and Shreve , S. 1984 . Connections between optimal control and singular control problems I, Monotone follower problems . SIAM J. Control Optim. , 22 ( 6 ) : 856 – 877 .
- Lions , P.L. and Sznitman , A.S. 1984 . Stochastic differential equations with reflecting boundary conditions . Comm. Pure Appl. Math. , 3 : 511 – 537 .
- Øksendal , B. and Sulem , A. 2005 . Applied Stochastic Control of Jumps Diffusions , Berlin : Springer .
- Peng , S. 1990 . A general stochastic maximum principle for optimal control problems . SIAM J. Control Optim. , 28 : 966 – 979 .
- Protter , P. 2003 . Stochastic Integration and Differential Equations , 2nd ed. , New York : Springer .
- Shreve , S.E. and Soner , H.M. 1994 . Optimal investment and consumption with transaction costs . Ann. Appl. Probab. , 4 : 609 – 692 .
- Yong , J. and Zhou , X.Y. 1999 . Stochastic Controls, Hamiltonian Systems and HJB Equations , New York : Springer Verlag .