Abstract
actuar is a package providing additional Actuarial Science functionality to the R statistical system. This paper presents the features of the package targeted at risk theory calculations. Risk theory refers to a body of techniques to model and measure the risk associated with a portfolio of insurance contracts. The main quantity of interest for the actuary is the distribution of total claims over a fixed period of time, modeled using the classical collective model of risk theory.
actuar provides functions to discretize continuous distributions and to compute the aggregate claim amount distribution using many techniques, including the recursive method and simulation. The package also provides various plotting and summary methods to ease working with aggregate models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
DAYKIN, C., PENTIKÄINEN, T. and PESONEN, M. (1994): Practical Risk Theory for Actuaries, Chapman and Hall, London.
DENUIT, M. and CHARPENTIER, A. (2004): Mathématiques de l’assurance non-vie, Vol. 1: Principes fondamentaux de théorie du risque, Economica, Paris.
DUTANG, C., GOULET, V. and PIGEON, M. (2008): actuar: An R package for actuarial science, Journal of Statistical Software 25 (7). http://www.jstatsoft.org/v25/i07
GERBER, H. U. (1979): An Introduction to Mathematical Risk Theory, Huebner Foundation, Philadelphia.
GOULET, V. and POULIOT, L.-P. (2008): Simulation of compound hierarchical models in R, North American Actuarial Journal 12, 401-412
GOULET, V. (2010): Evaluation of ruin probabilities using R and actuar. In preparation.
HOGG, R. V. and KLUGMAN, S. A. (1984): Loss Distributions, Wiley, New York.
KAAS, R., GOOVAERTS, M., DHAENE, J. and DENUIT, M. (2001): Modern actuarial risk theory, Kluwer Academic Publishers, Dordrecht.
KLUGMAN, S. A., PANJER, H. H. and WILLMOT, G. (2008): Loss Models: From Data to Decisions, Third Edition, Wiley, New York.
PANJER, H. H. (1981): Recursive evaluation of a family of compound distributions, ASTIN Bulletin 12, 22-26
R DEVELOPMENT CORE TEAM (2009): R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna. http://www.R-project.org
Acknowledgments
This research benefited from financial support from the Natural Sciences and Engineering Research Council of Canada and from the Chaire d’actuariat (Actuarial Science Chair) of Université Laval.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goulet, V. (2010). Computation of the Aggregate Claim Amount Distribution Using R and Actuar. In: Lechevallier, Y., Saporta, G. (eds) Proceedings of COMPSTAT'2010. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2604-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2604-3_13
Published:
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2603-6
Online ISBN: 978-3-7908-2604-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)