Continuous parametric distributions are useful tools for modeling and pricing insurance risks, measuring income inequality in economics, investigating reliability of engineering systems, and in many other areas of application. In this paper, we propose and develop a new method for estimation of their parameters—the method of Winsorized moments (MWM)—which is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for log-location-scale families and their variants, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their performance is also compared to that of MTM and the maximum likelihood estimators (MLE). In addition, the effect of model choice and parameter estimation method on risk pricing is illustrated using actual data that represent hurricane damages in the United States from 1925 to 1995. In particular, the estimated pure premiums for an insurance layer are computed when the lognormal and log-logistic models are fitted to the data using the MWM, MTM and MLE methods.

This paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (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), 1–22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.

The majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer's risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident.