Uncertain insurance risk process with single premium and multiple classes of claims

Abstract

Traditionally an insurance risk process is considered under the framework of probability theory with a prerequisite that the estimated distribution function is close enough to the real frequency. However, due to economic or technological reasons, sometimes data are unavailable or difficult to obtain, such as when we consider a new insurance product or insurance for valuable weapons. Under these situations, reimbursement policies are based on experts’ belief degree, which has a much wider range than the real frequency. As a result, we should employ uncertain insurance risk models to better deal with human uncertainty in running an insurance company. Noticing the fact that an insurance company pays for different kinds of risks and the uncertainty of the customer’s arrivals and payments, we investigate an uncertain insurance risk process with multiple classes of claims where the premium process follows an uncertain renewal process. Then we derive expressions for the ruin index and the uncertainty distribution of the ruin time. Some numerical examples and a real data example are performed to capture more insights.