Research projects

Project CEMAPRE internal

TitleThe impact of bonus-malus systems in finite and continuous time ruin probabilities in motor insurance for large portfolios. The open model.
ParticipantsLourdes B. Afonso, Agnieszka Bergel, Rui M.R. Cardoso, Alfredo Egídio dos Reis (Principal Investigator), Gracinda R. Guerreiro
SummaryWe 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.