Telematics data from usage-based motor insurance provide valuable information -including vehicle usage, attitude towards speeding, time and proportion of urban/non-urban driving -that can be used for ratemaking. Additional information on acceleration, braking and cornering can likewise be usefully employed to identify near-miss events, a concept taken from aviation that denotes a situation that may have resulted in an accident. We analyze near-miss events from a sample of drivers in order to identify the risk factors associated with a higher risk of near-miss occurrence. Our empirical application with a pilot sample of real usage-based insurance data reveals that certain factors are associated with a higher expected number of near-miss events, but that the association differs depending on the type of near-miss. We conclude that nighttime driving is associated with a lower risk of cornering events, urban driving increases the risk of braking events and speeding is associated with acceleration events. These results are relevant for the insurance industry in order to implement dynamic risk monitoring through telematics, as well as preventive actions.

This paper addresses a new problem in the literature, which is how to consider reserving issues for a portfolio of general insurance policies when there is excess-of-loss reinsurance. This is very important for pricing considerations and for decision making regarding capital issues. The paper sets out how this is currently often tackled in practice and provides an alternative approach using recent developments in stochastic claims reserving. These alternative approaches are illustrated and compared in an example using real data. The stochastic modelling framework used in this paper is Double Chain Ladder, but other approaches would also be possible. The paper sets out an approach which could be explored further and built on in future research.

A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.