On a Risk Model with Surplus-dependent Premium and Tax Rates |
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Authors: | Eric C K Cheung David Landriault |
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Institution: | 1. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong 2. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada
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Abstract: | In this paper, the compound Poisson risk model with surplus-dependent premium rate is analyzed in the taxation system proposed
by Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007). In the compound Poisson risk model, Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007) showed that a simple relationship between the ruin probabilities in the risk model with and without tax exists. This so-called
tax identity was later generalized to a surplus-dependent tax rate by Albrecher et al. (Insur Math Econ 44(2):304–306, 2009). The present paper further generalizes these results to the Gerber–Shiu function with a generalized penalty function involving
the maximum surplus prior to ruin. We show that this generalized Gerber–Shiu function in the risk model with tax is closely
related to the ‘original’ Gerber–Shiu function in the risk model without tax defined in a dividend barrier framework. The
moments of the discounted tax payments before ruin and the optimal threshold level for the tax authority to start collecting
tax payments are also examined. |
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