Publication

Abstract : This paper investigates the Gerber-Shiu function (G-SF) of the MAP/PH omega insurance risk process with level-dependent premium arrival. The omega model differentiates between ruin and bankruptcy, providing a more realistic assessment of an insurance company's financial stability. By incorporating Markovian arrival processes (MAPs) for claim arrivals and phase-type (PH) distributions for claim sizes, the MAP/PH omega risk model offers a robust framework for analysing risk. The level-dependent premium rate adjusts based on the insurer's reserve levels, making the model more flexible and applicable to real-world scenarios. We derive integro-differential equations for the G-SF, providing insights into the expected discounted penalty at bankruptcy. Numerical solutions demonstrate the model's practical applications, revealing that higher initial surpluses correlate with lower expected penalties and bankruptcy probabilities.