Generalized survival energy models with exogenous covariates for mortality prediction

Abstract

We develop a generalized survival energy model that relates mortality to social and economic conditions through a latent energy process. Death occurs when this process first reaches or crosses zero. Environmental covariates enter the coefficients governing depletion, recovery, fluctuations and accumulated damage, yielding lifetime distributions conditional on the environmental path. We derive these distributions for diffusion and inverse Gaussian specifications and describe their numerical evaluation. An application to Japanese male and female mortality data assesses predictive performance against Cairns--Blake--Dowd benchmarks. Conditional on realized environmental paths, the selected inverse Gaussian models achieve small prediction errors comparable to those of the benchmarks. The framework also provides a model-based interpretation of how environmental changes affect mortality through the rate of damage accumulation or the magnitude of energy fluctuations. These interpretations describe conditional statistical relationships rather than causal effects. The resulting models offer a way to study mortality under alternative environmental scenarios while retaining a connection to classical actuarial survival models.