Home Graphic and Numerical Evolution of a Bonus-Malus System via Markov Chain Models
Article
Licensed
Unlicensed Requires Authentication

Graphic and Numerical Evolution of a Bonus-Malus System via Markov Chain Models

  • Mohamed Yasser BOUNNITE EMAIL logo and Abdelaziz NASROALLAH
Published/Copyright: November 16, 2019

Abstract

This paper describes an online solution for visualizing the simulation of a discrete time Markov chain using an animated graph. Based on the D3.js library, the development of this solution offers the user the choice between a presentation based on the concept of a probabilistic graph oriented and a presentation of the transitions in a matrix framework. As an application the solution helps to describe the dynamics of individual policyholders in a Bonus-Malus system of automobile insurance.

JEL Classification: 60-08; 60Jxx; 62-09; 68-Rxx; 68-Uxx; 68-Wxx; 90-80

References

Barco-Rios, H., E. Rojas-Calderon, and E. Restrepo-Parra. 2011. “Graphic User Interface for Monte Carlo Simulation of Ferromagnetic/Antiferromagnetic Manganite Bilayers.” Tecno Logicas No. 26, ISSN 0123-7799, pp. 133–143.10.22430/22565337.53Search in Google Scholar

Bostock M., V. Ogievetsky, and J. Heer. 2011. “D3: Data-Driven Documents.” IEEE Transactions on Visualization and Computer Graphics 17 (12): 2301–09.10.1109/TVCG.2011.185Search in Google Scholar

Byrne J., C. Heavey, and P. J. Byrne. 2010. “A Review of Web-Based Simulation and Supporting Tools.” Simulation Modeling Practice and Theory 18 (3): 253–76.10.1016/j.simpat.2009.09.013Search in Google Scholar

David A., and C. J. M. Tauro. 2015. “Web 3D Data Visualization of Spatio Temporal Data Using Data Driven Document (D3.js).” International Journal of Computer Applications 111 (4): 42–46.10.5120/19529-1169Search in Google Scholar

Gonzalez, J. A., L. Jover, E. Cobo, and P. Munoz. 2010. “A Web-Basedlearning Tool Improves Student Performance in Statistics: A Randomized Masked Trial.” Computers and Education 55 (2): 704–13.10.1016/j.compedu.2010.03.003Search in Google Scholar

Ethier, S. N., and T. G. Kurtz. 2005. Markov Processes: Characterization and Convergence. Hoboken (New Jersey): John Wiely & Sons.Search in Google Scholar

Fernandez-Morales, A. 2015. “Application of a Discrete-Time Markov Chain Simulation in Insurance.” International Journal of Recent Contributions from Engineering, Science & IT (iJES) 3 (3): 27–32. http://dx.doi.org/10.3991/ijes.v3i3.4929.10.3991/ijes.v3i3.4929Search in Google Scholar

Lemaire, J., and H. Zi. 1994. “A Comparative Analysis of 30 Bonus-Malus Systems.” ASTlN Bulletin 24 (2): 287–309.10.2143/AST.24.2.2005071Search in Google Scholar

Lemaire, J. 1995. Bonus-Malus Systems in Automobile lnsurance. Boston: Kluwer Academic, Publisher.10.1007/978-94-011-0631-3Search in Google Scholar

Lemaire, J. 2004. Bonus-Malus system, Encyclopeadia of Actuarial Science, 184–91. NewYork: Wiley.10.1002/9780470012505.tab014Search in Google Scholar

Lunsford, M., G. H. Rowell, and T. Goodson-Espy. 2006. “Classroomresearch: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Postcalculus Probability and Statistics Classes.” Journal of Statistics Education 14 (3): 1–19.10.1080/10691898.2006.11910587Search in Google Scholar

Phil, H. Markov Chain Visualisation Tool. University of Edinburgh UK. Accessed August 5, 2018. http://homepages.inf.ed.ac.uk/jeh/Markov.Search in Google Scholar

Pitrebois, S., M. Denuit, and J. F. Walhin. 2003 “Bonus-Malus Scales in Segmented Tariffs: Gilde and Sundt’s Work Revisited.” Discussion Paper, 407, Institut de Statistique, Université Catholique de Louvain.Search in Google Scholar

Powell, V., and L. Lehe. “Markov Chains. A visual explanation.” Accessed August 11, 2018. http://setosa.io/blog/2014/07/26/markov-chains.Search in Google Scholar

Schneiter, K. 2008. “Two Applets for Teaching Hypothesis Testing.” Journal of Statistics Education 16 (3): 1–8.10.1080/10691898.2008.11889575Search in Google Scholar

Sosa, G. W., D. E. Berger, A. T. Saw, and J. C. Mary. 2011 “Effectiveness of Computer- Assisted Instruction in Statistics: A Meta-Analysis.” Review of Educational Research 81 (1): 97–127.10.3102/0034654310378174Search in Google Scholar

Varga, R. 1962. Matrix Iterative Analysis. Englewood Cliffs: Prentice Hall.Search in Google Scholar

Wang, P., B. K. Vaughn, and M. Liu. 2011. “The Impact of Animation Interactivity on Novices’ Learning of Introductory Statistics.” Computers & Education 56 (1): 300–11.10.1016/j.compedu.2010.07.011Search in Google Scholar

Wang, R., Y. Perez-Riverol, H. Hermjakob, and J. A. Vizcaíno. 2015. “Open Source Libraries and Frameworks for Biological Data Visualisation: A Guide for Developers.” Proteomics 15: 1356–74.10.1002/pmic.201400377Search in Google Scholar

West, R. W., and R. T. Ogden. 1998. “Interactive Demonstrations for Statistics Education on the World Wide Web.” Journal of Statistics Education 6 (3): 1–9.10.1080/10691898.1998.11910624Search in Google Scholar

Published Online: 2019-11-16

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 22.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/apjri-2018-0041/html
Scroll to top button