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novalis comments on Why is it rational to invest in retirement? I don't get it. - Less Wrong Discussion
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I wonder if there are any death insurance companies, where you give them your retirement savings, and when you retire they pay you money continuously until you die. That way, they can pay you extra to take into account that you might not live that long.
The question is how much you care about that person. Does having a worldline connecting you matter regardless of length? Does it matter at all? Do you care about them inversely to their chronological distance to you? There's not a particular rational answer. It's just a question of your values.
Yes; they are called annuities (well, some types of annuities work this way).
Wait annuities are tontines? Cool.
Not precisely tontines. For variable annuities, your return depends much more on the market (highly unpredictable) than on the deaths of other members (highly predictable, in aggregate). For fixed annuities, of course, your return is fixed.