Research projects

Project CEMAPRE internal

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