Project CEMAPRE internal
| Title | The impact of bonus-malus systems in finite and continuous time ruin probabilities in motor insurance for large portfolios. |
| Participants | Lourdes B Afonso, Rui M R Cardoso, Alfredo Egídio dos Reis (Principal Investigator), Gracinda R Guerreiro |
| Summary | In motor insurance ratemaking is twofold: "a priori" and "a posteriori". In the latter, premium calculation is based on past experience and brings a greater volatility. Typically, ruin probabilities are computed using the classical Cramér-Lundberg model where premium is paid continuously at a constant rate. Afonso et al. (2009) consider a model applicable to large portfolios where a varying premium is used by means of a mix of calculation and simulation. It differs from the usual literature, also, it allows to obtain fast results in a finite horizon and continuous time. The ideas in that model can be brought and applied in motor insurance ratemaking (experience rating) for two main reasons: Premium calculation is applied for large portfolios and it is based on past claim record. However, the model needs to be changed to fit in the features common in motor insurance. Usually, in motor insurance, experience rating changes the premium, as a function of the past claim number record only. Claim severities do not matter here, although they do for the ruin probility computation. the approach used is by a Markov chain procedure. The number of claims is used to determine the next rating class and calculate the applicable premium. That, together with the aggregate claims, is necessary to compute ruin probabilities for the portfolio. We measure the impact in the ruin probabilities of a bonus malus system (BMS), considering different known optimal scales (e.g. Norberg (1976), Borgan et al. (1981), Gilde & Sundt (1989), Andrade e Silva (1991) and Denuit & Dhaene(2001)), as well as real commercial scales. We will illustrate the computation of ruin probabilities using different claim frequency and severity distributions as well as BMS with different stationary times. We will use real data from automobile thirdparty liability portfolios of Portuguese insurers. First, we work a closed portfolio and then we will expand our model to an open portfolio, a more realistic situation. |