Introduction

Introduction#

GEMAct is an actuarial package, based on the collective risk theory framework, that offers a comprehensive set of tools for non-life (re)insurance costing, stochastic claims reserving, and loss aggregation.

The variety of available functionalities makes GEMAct modeling very flexible and provides users with a powerful tool that fits into the expanding community of Python programming language.

The accompanying paper is registered with DOI doi:10.1017/S1748499524000022.

APA citation:

Pittarello, G., Luini, E., & Marchione, M. M. (2024). GEMAct: a Python package for non-life (re)insurance modeling. Annals of Actuarial Science, 1–37. doi:10.1017/S1748499524000022

BibteX citation:

@article{Pittarello_Luini_Marchione_2024,
title={GEMAct: a Python package for non-life (re)insurance modeling},
DOI={10.1017/S1748499524000022},
journal={Annals of Actuarial Science},
author={Pittarello, Gabriele and Luini, Edoardo and Marchione, Manfred Marvin},
year={2024},
pages={1–37}}

The manuscript pre-print is instead available at ArXiV:2303.01129.

Scope#

  • A collective risk model apparatus for costing non-life (re)insurance contracts.

  • Extend the set of distributions available in scipy to actuarial scientists. GEMAct provides the first Python implementation of the (a, b, 0) and (a, b, 1) distribution classes.

  • Popular copulas with improved functionalities, e.g. the Student t copula cumulative distribution function can be numerically approximated.

  • A loss reserve estimation tool.

  • The first open-source Python implementation of the AEP algorithm.

Reinsurance Contracs#

GEMAct can be used for costing the following reinsurance contracts and their combinations.

  • Excess-of-Loss (XL) including:

    • individual and aggregate coverage modifers (cover and deductible),

    • reinstatements.

  • Quota-share (QS).

  • Stop-loss (SL).

  • Reinsurance Programme including:

    • drop-down and stretch-down layers.

    • retention layer with a maintenance limit.

Computational methods#

GEMAct offers multiple numerical methods used within the context of loss distributions approximation.

  • Collective risk model:

    • Recursive method (Panjer recursion),

    • Discrete Fourier transform, via the fast Fourier transform (FFT) algorithm,

    • Monte Carlo simulation,

    • Quasi-Monte Carlo simulation.

  • Loss (model) aggregation:

    • AEP algorithm,

    • Monte Carlo simulation.

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