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

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• 作者：Pierre-Olivier Goffard^a ; ^{pierre.olivier.goffard@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Sté ; phane Loisel^b ; ^{stephane.loisel@univ-lyon1.fr" class="auth_mail" title="E-mail the corresponding author} ; Denys Pommeret^c ; ^{denys.pommeret@univ-amu.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Compound Poisson model ; Ultimate ruin probability ; Natural exponential families with quadratic variance functions ; Orthogonal polynomials ; Gamma series expansion ; Laplace transform inversion
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：499-511
• 全文大小：981 K

文摘

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 a 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 discretization step of the claim sizes distribution. Finally, the coefficients of our formula do not depend on initial reserves.