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Introduction to the theory of optimal stopping

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Stochastic Control Theory and Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 16))

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References

  1. A. Bensoussan, Introduction to the theory of impulse control, in Control Theory and Topics in Functional Analysis, vol.3, International Atomic Energy Agency, Vienna, 1976.

    Google Scholar 

  2. A. Bensoussan, J.L. Lions, Problèmes de temps d'arret optimal et inéquations variationnelles paraboliques, Applicable Anal. 3(1973), 267–294.

    Google Scholar 

  3. A.Bensoussan and J.L.Lions, Temps d'Arret et Controle Impulsionnel, Herman, Paris, to appear.

    Google Scholar 

  4. J.M. Bismut, Dualité convexe, tmeps d'arret optimal et controle stochastique, Z. Wahrscheinlichkeitstheorie view. Gebiete, 38(1977), 169–198.

    Google Scholar 

  5. J.M. Bismut and B. Skalli, Temps d'arret optimal, théorie générale des processus et processus de Markov, Z. Wahrscheinlichkeits-theorie verw. Gebiete, 39(1977), 301–314.

    Google Scholar 

  6. R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, New York and London, Academic Press 1968.

    Google Scholar 

  7. Y.S. Chow, H. Robbins and D. Siegmund, Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin Comp., Boston, 1971.

    Google Scholar 

  8. H. Chernoff, Optimal stochastic control, Sankhya, ser.A, 30(1968), 221–252.

    Google Scholar 

  9. E.B.Dynkin, Markov Processes, Springer Verlag, 1965.

    Google Scholar 

  10. E.B. Dynkin, Optimal choice of a stopping time for a Markov process, Dokl.Akad.Nauk USSR, 150(1963), No.2, 238–240.

    Google Scholar 

  11. G. Engelbert, On optimal stopping rules for Markov processes with continuous time, Theory of Prob. and Appl., 19(1974), No.2, 289–307.

    Google Scholar 

  12. A. Engelbert, On ɛ-optimal Markov times for Markov processes with continuous time, Mathematische Nachrichten 70(1975), 251–257.

    Google Scholar 

  13. A.G. Fakeev, Optimal stopping rules for stochastic processes with continuous parameter, Theory of Prob. and Appl., 18(1973), No.2, 304–311.

    Google Scholar 

  14. W.Fleming, Optimal continuous parameter stochastic control, SIAM Review, 11(1969), No.4.

    Google Scholar 

  15. B.I. Griegelionis and A.N. Shiryaev, On controlled Markov processes and the Stefan problem, Problemy Peredachi Informacii, 4(1968), 60–72.

    Google Scholar 

  16. N.B. Krylov, Controlled Processes of Diffusion Type, Nauka, Moscow, 1977.

    Google Scholar 

  17. M.P. Mc Kean, A free boundary problem for the heat equation arising from a problem in Mathematical Economics, Industrial Management Review, 6(1965), 32–39.

    Google Scholar 

  18. J.F. Mertens, Processus stochastiques généraux et surmartingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 22(1972), 45–48.

    Google Scholar 

  19. J.F. Mertens, Strongly supermedian functions and optimal stopping, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 26(1973), 119–139.

    Google Scholar 

  20. U. Mosco, Introduction to variational and quasi-variational inequalities, in Control Theory and Topics in Functional Analysis, vol. 3, International Atomic Energy Agency, Vienna, 1976.

    Google Scholar 

  21. M. Nisio, On nonlinear semigroups for Markov processes associated with optimal stopping, Appl. Math. and Optimization 4 (1978) No.2, 143–169.

    Google Scholar 

  22. S.R. Pliska, A semigroup representation of the maximum expected reward vector in continuous parameter Markov decision theory, SIAM J. on Control 13(1975), No.6, 1115–1129.

    Google Scholar 

  23. M.Robin, Controle impulsionnel des processus de Markov, Thèse de Doctorat, l'Université Paris IX, 1978.

    Google Scholar 

  24. L.I.Rubinstein, Stefan's Problem, Riga, 1967.

    Google Scholar 

  25. P.A. Samuelson, Mathematics of speculative prices, SIAM Review, 15(1973), No.1, 1–42.

    Google Scholar 

  26. A.N. Shiryaev, Statistical Sequential Analysis, Nauka, Moscow, 1976, (in Russian).

    Google Scholar 

  27. I.L. Snell, Applications of martingale system theory, Trans. Amer. Math. Soc. 73(1953), 293–312.

    Google Scholar 

  28. T. Tobias, Optimal stopping of diffusion processes and parabolic variational inequalities, Diff. Equations, 9(1973), No.4, 702–708.

    Google Scholar 

  29. A. Wald, Sequential Analysis, Wiley, New York, 1947.

    Google Scholar 

  30. J. Zabczyk, A mathematical correction problem, Kybernetika, 8(1972), No.4, 317–322.

    Google Scholar 

  31. J. Zabczyk, Optimal control by means of switching, Studia Math. XLV(1973), 161–171.

    Google Scholar 

  32. J.Zabczyk, Stochastic control on Stock Exchange, CRM-803, Université de Montreal, 1978.

    Google Scholar 

  33. J. Zabczyk, Semigroup methods in stochastic control theory, CRM-821, Université de Montreal, 1978.

    Google Scholar 

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M. Kohlmann W. Vogel

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© 1979 Springer-Verlag

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Zabczyk, J. (1979). Introduction to the theory of optimal stopping. In: Kohlmann, M., Vogel, W. (eds) Stochastic Control Theory and Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009384

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  • DOI: https://doi.org/10.1007/BFb0009384

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09480-7

  • Online ISBN: 978-3-540-35211-2

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