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

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.
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Contributeur : Stéphane Loisel <>
Soumis le : lundi 10 novembre 2014 - 18:17:10
Dernière modification le : lundi 4 avril 2016 - 14:42:44
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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. 2014. 〈hal-00853680v2〉

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