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On optimal stopping of risk processes with regime switching. (English) Zbl 1267.91042

The paper is devoted to two problems of optimal stopping of a non-homogeneous risk process. It is assumed that, in both models, the main characteristics of the process changes according to unobservable random variable with given distribution. In the first model it is assumed that the post-disorder distributions are not known a priori (see e.g., A. S. Polunchenko and A. G. Tartakovsky, Methodol. Comput. Appl. Probab. 14, No. 3, 649-684 (2012; Zbl 06124706)]) and they are randomly chosen from a finite set of admissible distributions. The second model concentrates on a situation when more than one disorder is possible. For both models optimal stopping rules with respect to given utility function are constructed using dynamic programming methodology. The paper extends the results from E. Ferenstein and A. Pasternak-Winiarski [in: Annals of the International Society of Dynamic Games 11, 489–507 (2011; Zbl 1218.91078)].

MSC:

91B30 Risk theory, insurance (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
90C40 Markov and semi-Markov decision processes
90C39 Dynamic programming
62L15 Optimal stopping in statistics
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