BAYESIAN CONFIDENCE INTERVALS FOR THE NUMBER AND THE SIZE OF LOSSES IN THE OPTIMAL BONUS–MALUS SYSTEM

• Authors: Marcin Dudzinski , Konrad Furmanczyk , Marek Kocinski
• Languages of publication: EN

Abstracts

EN

Most of the so far proposed Bonus–Malus Systems (BMSs) establish a premium only according to the number of accidents, without paying attention to the vehicle damage severity. [Frangos and Vrontos 2001] proposed the optimal BMS design based not only on the number of accidents of a policyholder, but also on the size of loss of each accident. In our work, we apply the approach presented by Frangos and Vrontos to construct the Bayesian confidence intervals for both the number of accidents and the amount of damage caused by these accidents. We also conduct some simulations in order to create tables of estimates for both the numbers and the sizes of losses and to compute the realizations of the corresponding Bayesian confidence intervals. We compare the results obtained by using our simulation studies with the appropriate results derived through an application of an asymmetric loss function and its certain modification.93-104

Keywords

EN

optimal BMS; number of claims; severity of claims; Bayesian analysis; Bayesian confidence intervals asymmetric loss functions

• Publisher: Katedra Ekonometrii i Statystyki, Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
• Journal: Metody Ilościowe w Badaniach Ekonomicznych
• Year: 2013
• Volume: 14
• Issue: 1
• Pages: 93-104

Dates

published

2013

Contributors

author

Marcin Dudzinski

• Department of Applied Mathematics Warsaw University of Life Sciences – SGGW

author

Konrad Furmanczyk

• Department of Applied Mathematics Warsaw University of Life Sciences – SGGW

author

Marek Kocinski

• Department of Applied Mathematics Warsaw University of Life Sciences – SGGW

References

• Basu A.P., Ebrahimi N. (1991) Bayesian approach to life testing and reliability estimation using asymmetric loss function, Journal of Plann. and Inferen., 29, pp. 21-31.
• Bermudez L., Denuit M., and Dhaene J. (2001) Exponential bonus-malus systems integrating a priori risk classification, Journal of Actuarial Practice, 3, pp. 67-95.
• Dionne G., Vanasse C. (1989) A generalization of automobile insurance rating models: the negative binomial distribution with a regression component, ASTIN Bulletin, 19(2), pp.199-21
• Frangos N.E., Vrontos S.D. (2001) Design of optimal Bonus-Malus systems with a frequency and a severity component on an individual basis in automobile insurance, ASTIN Bulletin, 31(1), pp. 1-22.