Title: Gerber-Shiu analysis of the MAP/PH omega risk model with level-dependent premium rate

Authors: P.P. Sreeshamim; M.J. Jacob

Addresses: Department of Mathematics, National Institute of Technology Calicut, Kerala – 673601, India ' Department of Mathematics, National Institute of Technology Calicut, Kerala – 673601, India

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.

Keywords: MAP claim arrivals; phase-type; PH claims; bankruptcy probability; level-dependent premium rate; dividend barrier; Gerber-Shiu function; G-SF.

DOI: 10.1504/IJMOR.2026.155538

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.3, pp.382 - 399

Received: 31 Jul 2024
Accepted: 07 Sep 2024
Published online: 05 Aug 2026 *

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