TY - JOUR
T1 - Bonus–Malus systems with Weibull distributed claim severities
AU - Ni, Weihong
AU - Constantinescu, Corina
AU - Pantelous, Athanasios A.
N1 - Funding Information:
The authors would like to acknowledge Nicholas Frangos and Spyros Vrontos for the introduction to the topic, Dominik Kortschak and Bo Li for helpful remarks during the revision of this paper. Moreover, we would like to thank the anonymous reviewer for his/her suggestions, and the idea to consider the generalised BMS that integrates the a priori and a posteriori information on a individual basis. The authors also kindly acknowledge partial support from the RARE-318984 project, a Marie Curie IRSES Fellowship within the 7th European Community Framework Programme. The paper has received the Best Paper Award at the 2013 Perspectives on Actuarial Risks in Talks of Young researchers (PARTY) conference, Ascona, Switzerland, January 27th–February 1st.
Publisher Copyright:
© Institute and Faculty of Actuaries 2014.
PY - 2014/9
Y1 - 2014/9
N2 - One of the pricing strategies for Bonus–Malus (BM) systems relies on the decomposition of the claims’ randomness into one part accounting for claims’ frequency and the other part for claims’ severity. By mixing an exponential with a Lévy distribution, we focus on modelling the claim severity component as a Weibull distribution. For a Negative Binomial number of claims, we employ the Bayesian approach to derive the BM premiums for Weibull severities. We then conclude by comparing our explicit formulas and numerical results with those for Pareto severities that were introduced by Frangos & Vrontos.
AB - One of the pricing strategies for Bonus–Malus (BM) systems relies on the decomposition of the claims’ randomness into one part accounting for claims’ frequency and the other part for claims’ severity. By mixing an exponential with a Lévy distribution, we focus on modelling the claim severity component as a Weibull distribution. For a Negative Binomial number of claims, we employ the Bayesian approach to derive the BM premiums for Weibull severities. We then conclude by comparing our explicit formulas and numerical results with those for Pareto severities that were introduced by Frangos & Vrontos.
KW - Bayesian Estimator
KW - Bonus-Malus Systems
KW - Weibull Distribution
UR - https://www.scopus.com/pages/publications/84944049301
U2 - 10.1017/S1748499514000062
DO - 10.1017/S1748499514000062
M3 - Article
AN - SCOPUS:84944049301
SN - 1748-4995
VL - 8
SP - 217
EP - 233
JO - Annals of Actuarial Science
JF - Annals of Actuarial Science
IS - 2
ER -