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Ruin probabilities by Padé’s method: simple moments based mixed exponential approximations (Renyi, De Vylder, Cramér–Lundberg), and high precision approximations with both light and heavy tails

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Abstract

We revisit below Padé and other rational approximations for ruin probabilities, of which the approximations mentioned in the title are just particular cases. We provide new simple Tijms-type and moments based approximations, and show that shifted Padé approximations are quite successful even in the case of heavy tailed claims.

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Notes

  1. However, if required, best admissible approximations to non-admissible ones may be obtained by the package SOPE [17].

  2. This method itself exploits a rational approximation [29].

  3. Note however that these approximations are light-tailed; therefore, difficulties are to be expected in the case of heavy tailed Lévy measures. Other challenging cases are that of Lévy measures with compact support, or with atoms.

  4. This method bears some similarity to the Post-Widder method of inverting Laplace transforms, advocated by Jagerman, where \(\xi \rightarrow \infty \).

  5. http://webspn.hit.bme.hu/~telek/tools/butools/index.php

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Acknowledgements

We thank Ulysses Solon for useful comments.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, Université de Pau, 64000, Pau, France

    F. Avram

  2. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Permanent Campus Argul, Jatni, Khurda, Odisha, 752 050, India

    A. D. Banik

  3. Department of Computer Science, University of Turin, Corso Svizzera 185, 10149, Torino, Italy

    A. Horvath

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  1. F. Avram
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Correspondence to A. Horvath.

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Avram, F., Banik, A.D. & Horvath, A. Ruin probabilities by Padé’s method: simple moments based mixed exponential approximations (Renyi, De Vylder, Cramér–Lundberg), and high precision approximations with both light and heavy tails. Eur. Actuar. J. 9, 273–299 (2019). https://doi.org/10.1007/s13385-018-0180-8

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