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Optimal stopping time problem for a discrete time risk process Un = u + cn - (X1+... + Xn) is analyzed. At a random moment 9, which is unobserved, there is a change in common distribution of subsequent claim sizes X1, X2,.... In the case when | the mean of a new distribution of claim sizes is greater than the premium c there is a need I to stop the process to recalculate the premium. The existence of optimal stopping rule is proved and the way to find it efficiently is described.
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Czasopismo
Rocznik
Tom
Strony
423--432
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
autor
- Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
autor
- Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Bibliografia
- [1] T. Bojdecki, Probability maximizing approach to optimal stopping and its application to a disorder problem, Stochastics, 3 (1979), 61-71.
- [2] Y. S. Chow, H. Robbins and D. Siegmund, Great Expectations: The Theory of Optimal Stopping, Houghto n Mifflin, Boston, 1971.
- [3] E. Z. Ferenstein and A. Sierocinski, Optimal stopping of a risk process, Appl. Math., 24, 3 (1997), 335-342.
- [4] U. Jensen, Monotone stopping rules for stochastic processes in a semimartingale representation with applications, Optimization, 20, 6 (1989), 837-852.
- [5] U. Jensen, An optimal stopping problem in risk theory, Scand. Actuarial J., 2 (1997), 149-159.
- [6] A. N. Shiryaev, Optimal Stopping Rules, Springer-Verlag, New York, 1978.
- [7] A. Schottl, Optimal stopping of a risk reserve process with interest and, cost rates, J. Appl. Prob., 35 (1998), 115-123.
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Bibliografia
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bwmeta1.element.baztech-article-PWA1-0043-0022