A nonparametric sequential test with power 1 for the ruin probability in some risk models

In this paper we consider a nonparametric sequential test of power one for the Andersen risk model. The main motivation comes from applications to insurance, and in particular to the sequential control of the ruin probability of an insurance company. The properties of the proposed test are studied. In particular, it is shown that, under the alternative, both the stopping time of the test and its mean value are finite. Finally, approximations for the size of the test and for the expected value of the stopping time are provided.