An optimal stopping problem in risk theory. (English) Zbl 0888.62104

Summary: In classical risk theory often stationary premium and claim processes are considered. In some cases it is more convenient to model non-stationary processes which describe a movement from environmental conditions, for which the premiums were calculated, to less favorable circumstances. This is done by a Markov-modulated Poisson claim process. Moreover the insurance company is allowed to stop the process at some random time, if the situation seems unfavorable, in order to calculate new premiums. This leads to an optimal stopping problem which is solved explicitly to some extent.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62L15 Optimal stopping in statistics
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI


[1] Asmussen S., Scand. Actuarial J. pp 69– (1989) · Zbl 0684.62073
[2] Asmussen S., Mathematics of Operations Research 19 pp 410– (1994) · Zbl 0801.60091
[3] Brémaud P., Point processes and queues (1981)
[4] DOI: 10.2307/1427443 · Zbl 0811.62096
[5] DOI: 10.1007/978-1-4613-9058-9
[6] Grigelionis B., Liet. Matem. Rink. 1 pp 30– (1993)
[7] Jensen U., Mathematics of Operations Research 18 pp 645– (1993) · Zbl 0778.60031
[8] Schmidli H., Insurance Math. Econom. 16 pp 135– (1994) · Zbl 0837.62087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.