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On the dual risk model with tax payments

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  • Albrecher, Hansjörg
  • Badescu, Andrei
  • Landriault, David
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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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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4RV7Y78-1/2/2017bb9ebf1ac0c2ab7d507e8aeb9511
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 3 (June)
    Pages: 1086-1094

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1086-1094

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    Web page: http://www.elsevier.com/locate/inca/505554

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    References

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    1. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
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    Cited by:
    1. Yang, Chen & Sendova, Kristina P., 2014. "The ruin time under the Sparre-Andersen dual model," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 28-40.
    2. Avanzi, Benjamin & Cheung, Eric C.K. & Wong, Bernard & Woo, Jae-Kyung, 2013. "On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 98-113.
    3. Ng, Andrew C.Y., 2009. "On a dual model with a dividend threshold," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 315-324, April.

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