Project CEMAPRE internal
| Title | The impact of bonus-malus systems in finite and continuous time ruin probabilities in motor insurance for large portfolios. The open model. |
| Participants | Lourdes B. Afonso, Agnieszka Bergel, Rui M.R. Cardoso, Alfredo Egídio dos Reis (Principal Investigator), Gracinda R. Guerreiro |
| Summary | We refer to our 2016 BMS Project, see references below. In motor insurance portfolio 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. Practice ratemaking have different approaches that we have to consider for the calculation of ruin probabilities. 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, for the computation of finite time ruin probabilities. We adapted this model to be applied to experience rating with Bonus Malus systems (shortly, BMS) in motor insurance. In these systems, classical BMS, future premia depend on the year claim experience (claim counts only) to compute next year premia for the motor portfolios. The adaptation resulted in a paper produced in 2016 where we considered a classical BMS only, see Afonso et al. (2016). We measured the effect of a classical BMS in the ruin probabilities by considering an existing commercial scale and also different known optimal scales (e.g. Norberg (1976), Borgan et al. (1981), Gilde & Sundt (1989), Andrade e Silva (1991) and Denuit & Dhaene(2001)). We used real data from an automobile third party liability portfolio form a Portuguese insurer. Now, we aim at improving and developing the model to be applied to open portfolios and to less standard models, like mixed Poisson based claim frequency models. We may also consider systems also based on severities. |