A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

Pierre-Olivier Goffard 1, 2, * Stéphane Loisel 3 Denys Pommeret 1
* Auteur correspondant
1 IML - Institut de mathématiques de Luminy
2 AXA France
3 SAF - Laboratoire de Sciences Actuarielle et Financière
Abstract : A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Family with Quadratic Variance Function (NEF-QVF). The method is convenient in at least four ways. Firstly, it leads to a simple analytical expression of the ultimate ruin probability. Secondly, the implementation does not require strong computer skills. Thirdly, our approximation method does not necessitate any preliminary discretisation step of the claim sizes distribution. Finally, the coefficients of our formula do not depend on initial reserves.
Keywords : natural exponential families with quadratic variance functions ultimate ruin probability Compound Poisson model orthogonal polynomials Gamma series expansion Laplace transform inversion
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Article dans une revue
Journal of Computational and Applied Mathematics, Elsevier, 2015, 296 (April 2016), pp.499-511
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Dernière modification le : jeudi 7 février 2019 - 16:48:12
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Pierre-Olivier Goffard, Stéphane Loisel, Denys Pommeret. A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model. Journal of Computational and Applied Mathematics, Elsevier, 2015, 296 (April 2016), pp.499-511. 〈hal-00853680v2〉

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