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The density of the time of ruin in the classical risk model with a constant dividend barrier

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  • Li, Shuanming
  • Lu, Yi

Abstract

In this paper, we investigate the density function of the time of ruin in the classical risk model with a constant dividend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without dividend payments and the density of the time of ruin with dividend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical examples are given to illustrate our results.

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  • Li, Shuanming & Lu, Yi, 2014. "The density of the time of ruin in the classical risk model with a constant dividend barrier," Annals of Actuarial Science, Cambridge University Press, vol. 8(1), pages 63-78, March.
    • Handle: RePEc:cup:anacsi:v:8:y:2014:i:01:p:63-78_00
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    Cited by:

    1. Shuanming Li & Yi Lu & Can Jin, 2016. "Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 747-764, September.

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