Extreme value theorems of uncertain process with application to insurance risk model (Q1955464)

This is a further contribution to the author's uncertainty theory introduced in 2004 and 2007 (see [Uncertainty theory. An introduction to its axiomatic foundations. Berlin: Springer (2004; Zbl 1072.28012); Berlin: Springer (2007; Zbl 1141.28001)]). In the present paper he proves some extreme value theorems of so-called uncertain independent increment processes and provides their uncertainty distribution of the first hitting time. The author also presents an uncertain insurance model by assuming that the claim is a renewal reward process, and proves a ruin index theorem.