Connections between optimal stopping and singular stochastic control

Stochastic Processes and their Applications

Volumn 77, Issue 2, 1998, Pages 253-281

  Boetius, Frederik ^a   Kohlmann, Michael ^a  

^a UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

93E20, 60G40, 60G44, 90A16; Impulse control; Irreversible investment; Local times; Optimal stopping; Options; Singular control

Indexed keywords

EID: 0007526656     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00049-0     Document Type: Article

References (33)

1. Baldursson F.M. Singular stochastic control and optimal stopping. Stochastics. 21:1987;1-40.
2. Baldursson F.M., Karatzas I. Irreversible investment and industry equilibrium. Finance Stochastics. 1:1997;69-89.
3. Baras J.S., Elliott R.J., Kohlmann M. The partially observed stochastic minimum principle. SIAM J. Control Optim. 276:1989;1279-1292.
4. Bather, J.A., Chernoff, H., 1966. Sequential decisions in the control of a spaceship. Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability, vol. 3, pp. 181-207.
5. Beneš V.E., Shepp L.A., Witsenhausen H.S. Some solvable stochastic control problems. Stochastics. 4:1980;39-83.
6. Bensoussan, A., Lions, J.-L., 1984. Impulse Control and Quasi-Variational Inequalities. Trans-Inter-Scientia, Tonbridge.
7. Chow P.-L., Menaldi J.-L., Robin M. Additive control of stochastic linear systems with finite horizon. SIAM J. Control Optim. 236:1985;858-899.
8. Darling, R.W.R., 1992. Isotropic stochastic flows. In: Pinsky, M.A., Wihsturz, V. (Eds.), Diffusion Processes and Related Problems in Analysis, vol. 2. Birkhäuser, Boston, pp. 75-94.
9. Davis M.H.A., Norman A.R. Portfolio selection with transaction costs. Math. Oper. Res. 154:1990;676-713.
10. Dixit A.K., Pindyck R.S. Investment Under Uncertainty. 1994;Princeton Univ. Press, Princeton.
11. ElKaroui N., Karatzas, I., 1988. Probabilistic aspects of finite-fuel, reflected follower problems. Acta Appl. Math. 11, 223-258.
12. ElKaroui, N., Karatzas, I., 1991. A new approach to the Skorohod problem, and its applications. Stochastics Stochastics Rep. 34, 57-82.
13. Fleming W.H., Soner H.M. Controlled Markov Processes and Viskosity Solutions. 1993;Springer, New York.
14. Friedman A., 1976. Stochastic Differential Equations and Applications, vol. 2. Academic Press, New York.
15. Ikeda N., Watanabe S. Stochastic Differential Equations and Diffusion Processes. 1989;North-Holland, Amsterdam.
16. Karatzas I. The monotone follower problem in stochastic decision theory. Appl. Math. Optim. 7:1981;175-189.
17. Karatzas I. A class of singular stochastic control problems. Adv. Appl. Probab. 15:1983;225-254.
18. Karatzas I. Probabilistic aspects of finite fuel stochastic control. Proc. Natl. Acad. Sci. USA. 82:1985;5579-5581.
19. Karatzas I. Optimization problems in the theory of continuous trading. SIAM J. Control Optim. 276:1989;1221-1259.
20. Karatzas O., Shreve S.E. Connections between optimal stopping and singular stochastic control I. Monotone follower problems. SIAM J. Control Optim. 226:1984;856-877.
21. Karatzas I., Shreve S.E. Connections between optimal stopping and singular stochastic control II. Reflected follower problems. SIAM J. Control Optim. 234:1985;433-451.
22. Karatzas I., Shreve S.E. Equivalent models for finite-fuel stochastic control. Stochastics. 18:1986;245-276.
23. Karatzas I., Shreve S.E. Brownian Motion and Stochastic Calculus. 1994;Springer, New York.
24. Kobila T. Ø ., 1993. A class of solvable stochastic investment problems involving singular stochastic control. Stochastics Stochastics Rep. 43, 29-63.
25. Krylov N.V. Controlled Diffusion Processes. 1980;Springer, New York.
26. McDonald R., Siegel D. The value of waiting to invest. Quart. J. Economics. 101:1986;707-727.
27. Menaldi J.L., Taksar M.I. Optimal correction problem of a multidimensional stochastic system. Automatica. 252:1989;223-232.
28. Pindyck R.S., 1991. Irreversibility and the explanation of investment behaviour. In: Lund, D., Ø ksendal, B. (Eds.), Stochastic Models and Option Values. North-Holland, Amsterdam, pp. 129-141.
29. Protter P. Stochastic Integration and Differential Equations. 1990;Springer, Berlin.
30. Shiryayev A.N. Optimal Stopping Rules. 1978;Springer, New York.
31. Shreve S.E., 1988. An introduction to singular stochastic control. In: Fleming, W., Lions, P.-J. (Eds.), Stochastic Differential Systems, Stochastic Control Theory and Applications. Springer, New York, pp. 513-528.
32. Shreve S.E., Lehotzky J.P., Gaver D.P. Optimal consumption for general diffusions with absorbing and reflecting barriers. SIAM J. Control Optim. 221:1984;55-75.
33. Soner H.M., Shreve S.E. Regularity of the value function for a two-dimensional singular stochastic control problem. SIAM J. Control Optim. 274:1989;876-907.