Orthogonal polynomial expansions to evaluate stop-loss premiums

TL;DR

This paper introduces a numerical approach using Laguerre polynomial expansions to efficiently evaluate survival functions and stop-loss premiums in reinsurance, offering an alternative to traditional Laplace transform methods.

Contribution

The paper presents a novel polynomial expansion technique for calculating reinsurance premiums, improving computational efficiency and accuracy over existing methods.

Findings

The polynomial expansion method accurately estimates survival functions.

The approach outperforms Laplace transform inversion in speed and precision.

Numerical results validate the effectiveness of the proposed method.

Abstract

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.