Regularization and error estimate of infinite-time ruin probabilities for Cramer-Lundberg model

Xuan Tran Dong, Tuan Nguyen Huy, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article, we consider the problem of finding the ultimate ruin probability in the classical risk mode. Using Laplace transform inversion and Fourier transform, we obtain ultimate ruin probability of an insurance company. First, we show that this problem is ill-posed in the sense of Hadamard. Then, we apply the Tikhonov and truncation methods for establishing the approximate function for the ultimate ruin probability. Furthermore, convergence of the method, together with some examples, will be given. Finally, we present a numerical example to show efficiency of the method.

Original languageBritish English
Pages (from-to)3820-3831
Number of pages12
JournalMathematical Methods in the Applied Sciences
Volume41
Issue number10
DOIs
StatePublished - 15 Jul 2018

Keywords

  • ill-posed problem
  • Laplace transform inversion
  • ultimate ruin probabilities

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