Title: A Markovian risk model with possible by-claims and dividend barrier

Authors: P.P. Sreeshamim; M.J. Jacob; A.S. Dibu

Addresses: Department of Mathematics, National Institute of Technology Calicut, Kerala-673601, India ' Department of Mathematics, National Institute of Technology Calicut, Kerala-673601, India ' Department of Data Science and Statistics, Christ (Deemed to be University), Bangalore, Karnataka-560029, India

Abstract: A MAP/PH risk model with possible by-claims and a dividend barrier is considered. Along with the main claim, a by-claim also can occur with a certain probability but by-claims are settled only after an inquiry and hence delayed. The model is analysed considering associated Markovian fluid models under the original timeline and an auxiliary timeline. Systems of integro differential equations (IDE) are developed for the Gerber-Shiu function (GSF) and the total dividends paid until ruin. Explicit expressions are obtained for the GSF of the models without and then with the barrier. Expressions are also provided for the moments of the total dividends paid until ruin. A dividends-penalty identity is given. The method is numerically illustrated with a two-phase model and sensitivity analysis of the model is done by varying some of the parameters involved.

Keywords: MAP claim arrivals; phase type claims; by-claims; risk reserve process; dividend barrier; Lundberg equation; Gerber-Shiu function; GSF.

DOI: 10.1504/IJMOR.2023.135545

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.4, pp.475 - 501

Received: 12 Oct 2022
Accepted: 16 Oct 2022
Published online: 18 Dec 2023 *

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