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In the paper we use penalty method to approximate a number of general stopping problems over finite horizon. We consider optimal stopping of discrete time or right continuous stochastic processes, and show that suitable version of Snell's envelope can by approximated by solutions to penalty equations. Then we study optimal stopping problem for Markov processes on a general Polish space, and again show that the optimal stopping value function can be approximated by a solution to a Markov version of the penalty equation.
Wydawca
Czasopismo
Rocznik
Tom
Strony
309--323
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Institute Of Mathematics Polish Academy Of Sciences Sniadeckich 8 00-956 Warsaw, L.Stettner@impan.pl
Bibliografia
- [1] V. Barbu, C. Marinelli, Variational inequalities in Hilbert spaces with measures and optimal stopping problems, Appl. Math. Optim. 57 (2008), 237–262.
- [2] A. Bensoussan, J. L. Lions, Applications of Variational Inequalities in Stochastic Control, North Holland, 1982.
- [3] E. B. Dynkin, Markov Processes, Springer, 1965.
- [4] A. G. Fakeev, The optimal stopping of random processes with continuous time, Teor. Verojatnost. i Primenen. 15 (1970), 336–344.
- [5] G. Mazziotto, £. Stettner, J. Szpirglas, J. Zabczyk, On impulse control with partial observation, SIAM J. Control Optim. 26(4) (1988), 964–984.
- [6] P. A. Meyer, Probability and Potentials, Blaisdell, Waltham, Mass., 1966.
- [7] P. A. Meyer, Markov Processes, Research and Training School, Indian Statistical Institute (translation by MN Sastry), 1969.
- [8] J. Palczewski, £. Stettner, Finite horizon optimal stopping of time-discontinuous functionals with applications to impulse control with delay, SIAM J. Control Optim. 48 (2010), 4874–4909.
- [9] J. Palczewski, £. Stettner, Stopping of discontinuous functionals with the first exit time discontinuity, Stochastic. Process. Appl. 121 (2011), 2361–2392.
- [10] G. Peskir, A. Shriyaev, Optimal Stopping and Free Boundary Problems, Birkhäuser 2006.
- [11] M. Robin, Controle impulsionnel des processus de Markov (Thesis), University of Paris IX, 1978.
- [12] £. Stettner, Penalty method for finite horizon stopping problems, SIAM J. Control Optim. 49 (2011), 1078–1999.
- [13] £. Stettner, Discrete time approximation of continuous time stopping problems, O. Hernandez Lerma Festshrift, in Stochastic Systems: Optimization, Control, and Applications of Stochastic Systems, ed. Daniel Hernández-Hernández and J. Adolfo Minjárez-Sosa, to be published by Birkhäuser, 2012.
- [14] £. Stettner, J. Zabczyk, Strong envelopes of stochastic processes and a penalty method, Stochastics 4 (1981), 267–280.
- [15] J. Zabczyk, Stopping problems on Polish spaces, Ann. Univ. Mariae Curie-Skłodowska Sect. A 51 (1997), 181–199.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA4-0034-0029