On optimal stopping of a discrete time risk process

• Autorzy: Bobecka K. , Danielak K. , Ferenstein E. Z.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

optimal stopping; discrete risk process; Markov process

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 2
• Strony: 423--432
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Bobecka K.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

autor

Danielak K.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

autor

Ferenstein E. Z.

• 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.