Abstract:
Dirichlet Process Mixtures (DPM) are a flexible statistical tool which entails a regularization to non-parametric modelling techniques. In this talk, we focus on the development of regression models for the distribution of dependent time to events, where DPMs are used to account for dependence among these. We consider two common applications in actuarial science: the analysis of competing risk events, and the analysis of dependent lifetimes.
For the analysis of competing risk events, the joint distribution of the time to events is characterized by a random effect, whose distribution follows a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud & Dutang (2018).
The analysis of dependent lifetimes, such as husband and wife couples, develops the framework further by considering the effect of couple-specific covariates within the dependence relationship. The Dirichlet Process Mixture-based regression framework is therefore enriched to account simultaneously for both individual as well as group-specific covariates. The approach allows to account for right censoring and left truncation as typical of survival analysis. The model is illustrated to jointly model the lifetime of male-female couples in a portfolio of joint and last survivor annuities of a Canadian life insurer as analysed by Frees et. Al. (1996).
The models show an improved in-sample and out-of-sample performance compared to traditional approaches assuming independent time to events. Furthermore, these offer additional insights on determinants of the dependence between time to events.