On the dual risk model with tax payments |
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| Authors: | Hansjrg Albrecher Andrei Badescu David Landriault |
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| Institution: | aRadon Institute, Austrian Acadamy of Sciences, Austria;bDepartment of Financial Mathematics, University of Linz, Altenbergerstrasse 69, 4040 Linz, Austria;cDepartment of Statistics, University of Toronto, 100 St. George Street, Toronto, Canada;dDepartment of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada |
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| Abstract: | In this paper, we study the dual risk process in ruin theory (see e.g. Cramér, H. 1955. Collective Risk Theory: A Survey of the Theory from the Point of View of the Theory of Stochastic Processes. Ab Nordiska Bokhandeln, Stockholm, Takacs, L. 1967. Combinatorial methods in the Theory of Stochastic Processes. Wiley, New York and Avanzi, B., Gerber, H.U., Shiu, E.S.W., 2007. Optimal dividends in the dual model. Insurance: Math. Econom. 41, 111–123) in the presence of tax payments according to a loss-carry forward system. For arbitrary inter-innovation time distributions and exponentially distributed innovation sizes, an expression for the ruin probability with tax is obtained in terms of the ruin probability without taxation. Furthermore, expressions for the Laplace transform of the time to ruin and arbitrary moments of discounted tax payments in terms of passage times of the risk process are determined. Under the assumption that the inter-innovation times are (mixtures of) exponentials, explicit expressions are obtained. Finally, we determine the critical surplus level at which it is optimal for the tax authority to start collecting tax payments. |
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