Uncertain insurance risk process with multiple classes of claims

Abstract

Traditionally, an insurance risk process describes an insurance company’s risk through some criteria using the historical data under the framework of probability theory with the prerequisite that the estimated distribution function is close enough to the true frequency. However, because of the complexity and changeability of the world, economical and technological reasons in many cases enough historical data are unavailable and we have to base on belief degrees given by some domain experts, which motivates us to include the human uncertainty in the insurance risk process by regarding interarrival times and claim amounts as uncertain variables using uncertainty theory. Noting the expansion of insurance companies’ operation scale and the increase of businesses with different risk nature, in this paper we extend the uncertain insurance risk process with a single class of claims to that with multiple classes of claims, and derive expressions for the ruin index and the uncertainty distribution of ruin time respectively. As the ruin time can be infinite, we propose a proper uncertain variable and the corresponding proper uncertainty distribution of that. Some numerical examples are documented to illustrate our results. Finally our method is applied to a real-world problem with some satellite insurance data provided by global insurance brokerage MARSH.