Dying Asymptotically2 July 2015
It seems as if most economists do not know how to handle death.
What I here mean is not that they don't cope well with the deaths of loved ones or with their own mortality — though I suspect that they don't. What I mean is that their models of the very long-run are over-simply conceived and poorly interpretted when it comes to life-spans.
In the typical economic model of the very long-run, agents either live forever, or they live some fixed span of time, and then die. Often, economists find that a model begins to fit the real world better if they change it from assuming that people live that fixed amount of time to assuming that people live forever, and some economists then conclude that people are irrationally assuming their own immortality.
Here's a better thought. In the now, people are quite sure that they are alive. They are less sure about the next instant, and still less sure about the instant after that. The further that they think into the future, the less their expectation of being alive … but there is no time at which most people are dead certain that their lives will have ended. (If I asked you, the reader, how it might be possible for you to be alive in a thousand years, chances are that you could come up with some scenario.)
On the assumption that personalistic probabilities may be quantified, then, imputed probabilities of being alive, graphed against time, would approach some minimum asymptotically. My presumption would be that the value thus approached would be 0 — that most people would have almost no expectation of being alive after some span of years. But it would never quite be zero.
While I'm sure that some models will only work on the assumption that people impute absolute certainty to being alive forever, I suspect that an awful lot of models will work simply by accepting that most people embrace neither that madness nor the madness of absolute certainty that they will be dead at some specific time. Other models may need a more detailed description of the probability function.
As I've perhaps said or implied somewhere in this 'blog; I don't think that real-life probabilities are usually quantified; I would therefore be inclined to resist adopting a model with quantified probabilities, though such toys can be very useful heuristics. The weaker notion that probabilities are an incomplete preördering would correspond to some weaker notion than an asymptotic approach, but I haven't given much thought to what it would be.