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The Perturbed Sparre Andersen Model with Interest and a Threshold Dividend Strategy

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  • Wei Wang

    (Tianjin Normal University)

Abstract

In this paper, we consider a Sparre Andersen model perturbed by diffusion (in which the inter-claim times are generalized Erlang(n)-distributed) with a constant interest under a threshold dividend payment strategy. Under such a strategy, no dividends are paid if the insurer’s surplus is below a certain threshold level. When the surplus is above the threshold level, part of the premium income and all of the interest income are paid out as dividends. Integro-differential equations with certain boundary conditions for the moment generating functions and moment functions of the present value of all dividends until ruin are derived. We also derive the integro-differential equations with boundary conditions for the Gerber–Shiu functions. Explicit expressions are given in terms of some functions related to high order integro-differential equations when the inter-claim times are Erlang(2) and Erlang(1) distributed.

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  • Wei Wang, 2015. "The Perturbed Sparre Andersen Model with Interest and a Threshold Dividend Strategy," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 251-283, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9332-0
    DOI: 10.1007/s11009-013-9332-0
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    References listed on IDEAS

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    Cited by:

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    2. Zhongqin Gao & Jingmin He & Zhifeng Zhao & Bingbing Wang, 2022. "Omega Model for a Jump-Diffusion Process with a Two-Step Premium Rate and a Threshold Dividend Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 233-258, March.

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