Orthogonal polynomial expansions to evaluate stop-loss premiums

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

1 SAF - Laboratoire de Sciences Actuarielle et Financière

A numerical method is proposed to evaluate the survival function of a compound distribution and the stop-loss premiums associated with a non-proportional global reinsurance treaty. The method relies on a representation of the probability density function in terms of Laguerre polynomials and the gamma density. We compare the method against a well established Laplace transform inversion technique at the end of the paper.

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

Domaines: Probabilités [math.PR]

Pierre-Olivier Goffard, Patrick J. Laub. Orthogonal polynomial expansions to evaluate stop-loss premiums. Journal of Computational and Applied Mathematics, 2020, 370, ⟨10.1016/j.cam.2019.112648⟩. ⟨hal-01626545v3⟩