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Risks 2018, 6(4), 110; https://doi.org/10.3390/risks6040110

Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

1
Department of Mathematics, Central Washington University, 400 East University Way, Ellensburg, WA 98926, USA
2
Department of Mathematics, Oregon State University, Corvallis, OR 97331-4605, USA
*
Author to whom correspondence should be addressed.
Received: 17 August 2018 / Revised: 25 September 2018 / Accepted: 27 September 2018 / Published: 1 October 2018
(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)
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Abstract

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin. View Full-Text
Keywords: ruin probability; dual risk model; constant interest rate; integral equation; Laplace transform; numerical approximation ruin probability; dual risk model; constant interest rate; integral equation; Laplace transform; numerical approximation
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Loke, S.-H.; Thomann, E. Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments. Risks 2018, 6, 110.

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