Stochastic loss reserving with mixture density neural networks

In recent years, new techniques based on artificial intelligence and machine learning in particular have been making a revolution the work of actuaries, including loss reserving. A particularly promising technique is that neural networks, which shown to offer versatile, flexible accurate approach However, applications networks reserving date primarily focused (important) problem fitting central estimates outstanding claims. practice, properties regarding variability claims are equally important (e.g., quantiles for regulatory purposes). this paper we fill gap by applying Mixture Density Network (“MDN”) The combines network architecture with mixture Gaussian distribution achieve simultaneously an estimate along distributional choice. Model done using rolling-origin approach. Our consistently outperforms classical over-dispersed model both interest, when applied wide range simulated environments various complexity specifications. We further extend MDN proposing two extensions. Firstly, present hybrid GLM-MDN called “ResMDN“. This balances tractability ease understanding traditional GLM one hand, additional accuracy flexibility provided other. show it can successfully improve errors baseline ccODP, although there generally performance compared examples considered. Secondly, allow explicit projection constraints, so actuarial judgement be directly incorporated into modelling process. Throughout, focus aggregate triangles, our methodologies tractable, they out-perform approaches even relatively limited amounts data. use data—to validate properties, real illustrate ascertain practicality approaches.