Conformal prediction regions for dependent censored lifetimes
Abstract
Joint-life insurance and annuity benefits depend on two or more dependent lifetimes, which portfolio data observe only up to a valuation date. Given the covariates of a new contract, such as the entry ages of a couple, we construct one lower bound per remaining lifetime such that, with at least a prespecified probability, every life survives beyond its bound. The first step is to characterize the functions which allow for a useful projection from a multivariate to a univariate setting. The construction then relies on univariate conformal prediction, which calibrates any fitted model on held-out data, so that this statement does not rely on a correct mortality or dependence model. Censoring is handled by calibrating on the contracts observed for at least a fixed horizon, weighted by the inverse of their probability of being observed that long. We show that, when the lives can be censored at different times, this is possible precisely for joint statements that every life survives beyond its own bound, and that a common censoring time also permits bounds on the second-death time. If censoring is independent of the lifetimes given the covariates, coverage holds for every sample size when these probabilities are known, and approximately in large samples when they or the conditional lifetime quantiles are estimated consistently. As an application, we analyze a Canadian joint-life annuity portfolio.