Entropy, longevity and the cost of annuities

This paper presents an extension of the application of the concept of entropy to annuity costs. Keyfitz (1985) introduced the concept of entropy, and analysed this in the context of continuous changes in life expectancy. He showed that a higher level of entropy indicates that the life expectancy has a greater propensity to respond to a change in the force of mortality than a lower level of entropy. In other words, a high level of entropy means that further reductions in mortality rates would have an impact on measures like life expectancy. In this paper, we apply this to the cost of annuities and show how it allows the sensitivity of the cost of a life annuity contract to changes in longevity to be summarized in a single figure index.