Actuarial Bayesian nonparametric regression modelling for survival data

This paper introduces a flexible regression model for the statistical analysis of the individual mortality profile of pension scheme members. The model incorporates individual-specific random effects, which follow a discrete distribution drawn from a Dirichlet Process, enhancing its adaptability to complex data structures. This results in a Dependent Dirichlet Process mixture model in the spirit of De Iorio et al. (Biometrics 65(3):762–771. https://doi.org/10.1111/j.1541-0420.2008.01166.x, 2009), which accommodates nonmonotonic relationships between covariates and the regression function. The application of the model is illustrated through the analysis of a mid-sized UK pension scheme dataset. The model shows the ability to capture complex features of the data, such as the late life mortality deceleration at no cost in terms of model parsimony, and an improved out-of-sample performance compared with standard parametric alternatives, making it particularly suitable for actuarial modelling applications.