Calculating Premium Credibility Using the Buhlmann-Straub Modelwith Nonparametric Assessment

Dwi Susanti; Sokono Sukono

doi:10.47194/ijgor.v1i1.15

Authors

Dwi Susanti
dwi.susanti@unpad.ac.id
Sokono Sukono

Keywords:

Buhlmann-Straub Model, Credibility Theory, Credibility Premium, General Insurance, Aggregate Claim Amount.

Abstract

When an insurance company calculates the premium it will divides the policy holders into groups. The division is considered based on risk level in each group. The problem is then to devise a way of combining the experience risk of the group with the experience of the individual risk to calculate the premium, so then Credibility Theory provides a solution to this problem.This script discuss about calculation of credibility premium use Buhlmann-Straub Model with nonparametric estimation to the aggregate claim amount data set within few years observation in some group of policy holders inÂ general insurance. By using credibility theory we can calculate the value of credibility factor and credibility premium or future premium. The value of premium credibility is calculated from only one group of policyholders from the previous year's data. For better value of premium credibility, data with more experience years and the policyholder group better reflect the total loss value during the observation year.The result of this calculation are credibility factor per group, average credibility premium per members in group and credibility premium total for the last year for each group. We can obtain total losses and total premium which surprisingly equal.Â

References

Budd, J., McCall, B., 2004. Unions and unemployment insurance benefits receipt: Evidence from the current population survey. Ind. Relations 43, 339â€“355.

Chantarat, S., Mude,A.G., Barrett,C.B., Carter,M.R. (2013) Designing index-based livestockinsurance for managing asset risk in Northern Kenya. The Journal of Risk and Insurance80 (1): 205-237.

Clement, K. Y., Wouter Botzen, W. J., Brouwer, R., & Aerts, J. C. J. H. (2018). A global review of the impact of basis risk on the functioning of and demand for index insurance. International Journal of Disaster Risk Reduction, 28, 845â€“853. doi:10.1016/j.ijdrr.2018.01.001

Goda, K., & Ren, J. (2013). Seismic risk management of insurance losses using extreme value theory and copula.Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, 760â€“786. doi:10.1533/9780857098986.5.760

Goovaerts, M.J., Kaas R., Van Heerwaarden, A.E. &Bauwelinckx,T. 1990 . Effective Actuarial Methods. Amsterdam : Elsevier Science Ltd.

Groot, N. Y., &Klaauw B. V. D. (2019). The effects of reducing the entitlement period to unemployment insurancebenefits. Labour Econimics, 57, 195-208. https://doi.org/10.1016/j.labeco.2019.02.003

Hao, M., Macdonald, A. S., Tapadar, P., & Thomas, R. G. (2016) Insurance loss coverage underrestricted risk classification: The case of iso-elastic demand. ASTIN Bulletin.

Hao, M., Macdonald, A. S., Tapadar, P., & Thomas, R. G. (2018). Insurance loss coverage and demand elasticities. Insurance: Mathematics and Economics, 79, 15â€“25.

Kass, R., Goovaerts,.M., Dhaene, Jan., & Kluwer, M. D. 2000. Modern Actuarial Risk Theory. Boston : Academic Publisher.

Kim, J. H. T., & Jeon, Y. (2013). Credibility theory based on trimming. Insurance: Mathematics and Economics,53(1), 36â€“47. doi:10.1016/j.insmatheco.2013.03.012

Klugman,S.A., Panjer,H.,.Harry., &Willmot, E.Gordon .1998. Loss Models: Data to Decisions. New York : A Wiley Interscience Publication.

Punzo, A., Bagnato, L., &Maruotti, A. (2018). Compound unimodal distributions for insurance losses. Insurance: Mathematics and Economics, 81, 95â€“107. doi:10.1016/j.insmatheco.2017.10.007

Outreville, J. (1998). Insurance Concepts. Theory and Practice of Insurance, pp. 131-146,springer ISBN: 978-1-4615-6187-3. DOI: 10.1007/978-1-4615-6187-3.