Applications of Convex Optimisation in Premium Rating

In this paper we discuss the application of modern mathematical optimization techniques to some of the common problems in insurance premium rating. The computationally tractable setting of convex optimization [6] is particularly attractive as it encompasses parameter estimation in generalized linear models and offers means to address practica lchallenges such as variable selection, coefficient smoothing, spatial and hierarchical priors, constraints on relativities and the time evolution of model parameters. Recent advances in modelling systems for convex optimization make these methods not only eminently practical but also in many respects more flexible than what is presently offered by statistical software.

Keywords: Convex optimization, generalized linear models, credibility, graduation, spatial smoothing, dynamic regression, revenue management.