Abstract
AbstractWe propose a new approach to mortality prediction under survival energy hypothesis (SEH). We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero. This study assumes that SE follows a time-inhomogeneous diffusion process and defines the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is a fictitious construct, we illustrate that this assumption has the potential to yield a good parametric family of cumulative probability of death, and the parametric family yields surprisingly good predictions for future mortality rates.
Highlights
WHY DOES A HUMAN DIE?Mortality prediction is an important social problem
We extend the toy model to a more general time-inhomogeneous diffusion process in a natural way and propose a specific model that can give the explicit form of the hitting time distribution function, which is called the mortality function
To understand the structural approach that we use, let us consider a simple example of an survival energy (SE) model (SEM)
Summary
Mortality prediction is an important social problem. The most popular mortality prediction model is the Lee–Carter model (Lee and Carter, 1992), which is based on death rates. Which can be the F-stopping time under some regularities and the probability of death up to time t is given by qc(t) = P(τ c ≤ t), t > 0 Our analysis is essentially the one for the first hitting time to zero of the SE process X c which is the basic structure for human beings We call this approach a (cohort-wise) structural approach to mortality prediction after the earlier literatures.
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