PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 69 | 1 |
Tytuł artykułu

A multidimensional singular stochastic control problem on a finite time horizon

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.
Rocznik
Tom
69
Numer
1
Opis fizyczny
Daty
wydano
2015
online
2015-11-30
Twórcy
Bibliografia
  • Budhiraja, A., Ross, K., Existence of optimal controls for singular control problems with state constraints, Ann. Appl. Probab. 16, No. 4 (2006), 2235–2255.
  • Chow, P. L., Menaldi, J. L., Robin, M., Additive control of stochastic linear systems with finite horizon, SIAM J. Control Optim. 23, No.6 (1985), 858–899.
  • Dufour, F., Miller, B., Singular stichastic control problems, SIAM J. Control Optim. 43, No. 2 (2004), 708–730.
  • Evans, L. C., Partial Differential Equations, American Mathematical Society, Providence, RI, 1998.
  • Fleming, W. H., Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer, New York, 2006.
  • Haussman, U. G., Suo, W., Singular optimal stochastic controls. I. Existence, SIAM J. Control Optim. 33, No. 3 (1995), 916–936.
  • Karatzas, I., Shreve, S. E., Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1988.
  • Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part I: The Skorokhod problem, SIAM J. Control Optim. 38, No. 5 (2000), 1603–1622.
  • Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part II: The radially symmetric case. Ergodic control, SIAM J. Control Optim. 39, No. 2 (2000), 635–659.
  • Krylov, N. V., Controlled Diffusion Processes, Springer-Verlag, New York, 1980.
  • Menaldi, J. L., Taksar, M. I., Optimal correction problem of a multidimensional stochastic system, Automatica J. IFAC 25, No. 2 (1989), 223–232.
  • Rudin, W., Functional Analysis, McGraw-Hill Book Company, New York, 1991.
  • Rudin, W., Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1976.
  • Soner, H. M., Shreve, S. E., Regularity of the value function for a two-dimensional singular stochastic control problem, SIAM J. Control Optim. 27 (1989), 876–907.
  • Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control, Applied stochastic analysis (London, 1989), Stochastics Monogr. 5, Gordon and Breach, New York, 1991, 265–301.
  • Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control: the parabolic case, Comm. Partial Differential Equations 16 (1991), 373–424.
  • S. A. Williams, P. L. Chow and J. L. Menaldi, Regularity of the free boundary in singular stochastic control, J. Differential Equations 111 (1994), 175–201.
  • http://en.wikipedia.org/wiki/Gronwall’s inequality, 24.09.2013.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2015_69_1_23
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.