Investigation of a Non-Linear Cramér-Lundberg Risk Model

Abstract

In this study, a non-linear version of a Cramér-Lundberg risk model is examined. The objective of this work is to evaluate the ruin probability of a non-linear risk model. The classical linear Cramér-Lundberg model has been widely studied in the literature. However, the linear model is not always realistic. Because an insurance company's premium income cannot always increase linearly. Therefore, it is recommended to adapt premium income as a function which increases monotonically and yet its rate of growth decreases over time. Thus, to account for this, a more realistic non-linear mathematical model has been constructed and investigated, when the premium income function is p(t)=c?t. Then Lundberg type upper bound was calculated for the ruin probability for the model under investigation.