On a multi-threshold compound Poisson surplus process with interest |
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Authors: | Ilie-Radu Mitric Kristina P Sendova |
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Institution: | 1. Department of Statistical and Actuarial Sciences , University of Western Ontario , London, ON, Canada imitric@uwo.ca;3. Department of Statistical and Actuarial Sciences , University of Western Ontario , London, ON, Canada |
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Abstract: | We consider a multi-threshold compound Poisson surplus process. When the initial surplus is between any two consecutive thresholds, the insurer has the option to choose the respective premium rate and interest rate. Also, the model allows for borrowing the current amount of deficit whenever the surplus falls below zero. Starting from the integro-differential equations satisfied by the Gerber–Shiu function that appear in Yang et al. (2008), we consider exponentially and phase-type(2) distributed claim sizes, in which cases we are able to transform the integro-differential equations into ordinary differential equations. As a result, we obtain explicit expressions for the Gerber–Shiu function. |
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Keywords: | Compound Poisson model Gerber-Shiu function Non-homogenous integro-differential equation |
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