Perturbed MAP/PH Risk Model With Possible Delayed By-Claims and a Constant Dividend Barrier - Sreeshamim, P. P.; Jacob, M. J. (Communications in Mathematics and Applications, 2024)
In this study, we consider a perturbed risk model with MAP claim arrivals, PH claim sizes that incorporates possible by-claims and dividend barrier affected by a Brownian motion. The by-claims can occur along with the main claim, but their settlement is always delayed due to some necessary investigation. In order to analyze the model, we consider associated Markovian fluid models defined in the original timeline and an auxiliary timeline. We develop systems of second order integro-differential equations (IDE) for the Gerber-Shiu functions (GSF) of both the models without as well as with the barrier and solve them explicitly. Working on the same line we derive expressions for the Moment of the total dividends paid until ruin. Furthermore, a dividends-penalty identity is established. To showcase the effectiveness of the method, we numerically illustrate it using a two-phase model. Finally, we conduct a sensitive analysis by varying some of the parameters involved in the model.
Keywords: MAP claim arrivals; Phase type claims; By-claims; Risk reserve process; Brownian motion; Dividend barrier; Lundberg equation; Gerber-Shiu function (GSF)