Finding Efficient Recursions for Risk Aggregation by Computer Algebra

TL;DR

This paper introduces finite-order recursions for risk aggregation probabilities using computer algebra, enabling linear-time computation under algebraic and D-finite assumptions on generating functions.

Contribution

It presents a novel method for deriving finite-order recursions for risk sums, improving computational efficiency over traditional approaches.

Findings

Recursions are of finite order, allowing linear-time computation.

Applicable to claim size with algebraic generating functions.

Applicable to claim number distributions with D-finite generating functions.

Abstract

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the assumption that the probability generating function of the claim size be algebraic. The probability generating function of the claim number is supposed to be from the rather general class of D-finite functions.