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On optimal stopping of risk processes with regime switching

Ferenstein E., Pasternak Winiarski A.

Demonstratio Mathematica

2012

Vol. 45, nr 2

435-454

In the paper we solve a problem of optimal stopping of a risk process in two alternative settings. We assume that the main characteristics of the risk process change according to unobservable random variable. In the first model we assume that the post-disorder distributions are not known a'priori and 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.

On some kind of Dynkin's stopping game

Ferenstein E.

Demonstratio Mathematica

2001

Vol. 34, nr 1

191-197

On nonzero-sum stopping game related to discrete risk processes

Bobecka K., Ferenstein E.

Control and Cybernetics

2001

Vol. 30, no 3

339-354

We consider two-person nonzero-sum stopping game. The players (insurers) observe discrete time risk processes until one of them decides to stop his process. Strategies of the players are stopping times. The aim of each player is to maximize his expected gain. We find Nash equilibrium point for this game under certain assumptions on reward sequences.