Two numerical methods to evaluate stop-loss premiums

Pierre-Olivier Goffard (1) , Patrick J. Laub (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

Two numerical methods are proposed to numerically evaluate the survival function of a compound distribution and the stop-loss premiums associated with a non-proportional global reinsurance treaty. The first method relies on a representation of the probability density function in terms of Laguerre polynomials and the gamma density, the second is a numerical inversion of the Laplace transform. Numerical comparisons are conducted at the end of the paper. MSC 2010: 60G55, 60G40, 12E10.

Mots clés: Risk theory; orthogonal polynomials; numerical Laplace transform inversion; reinsurance; stop-loss premium

Domaines: Probabilités [math.PR]

Pierre-Olivier Goffard, Patrick J. Laub. Two numerical methods to evaluate stop-loss premiums. 2017. ⟨hal-01626545v1⟩