On the efficient evaluation of ruin probabilities for completely monotone claim distributions. (English) Zbl 1201.91088
In this article the quick numerical evaluations of ruin probabilities and tails of aggregate claims are a challenge in the presence of heavy tails are considered. The authors show that a quadrature method due to L. N. Trefethen, J. A. C. Weideman and T. Schmelzer [BIT 46, No. 3, 653–670 (2006; Zbl 1103.65030)] is well suited for the evaluation of the integrals that appear in the inverse Laplace transform of these quantities. For quantities those can be expressed as the Laplace transform of a signed measure \(\mu\). A theoretical justification is given by establishing the error bounds. A special case for which this situation applies is the calculation of ruin probabilities and tails of compound Poisson aggregate claim tails for completely monotone claim distribution. This method in particular provides an efficient alternative to a related method proposed by O. Thorin [Skand. Aktuarietidskr. 1973, 100–119 (1973; Zbl 0283.60098)]. A number of numerical illustrations are considered.
Reviewer: C. L. Parihar (Indore)
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91G80 | Financial applications of other theories |
| 91G60 | Numerical methods (including Monte Carlo methods) |
References:
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