With uncertainty about that extinction rate this Weitzman paper’s argument is relevant:
A critical feature of the distant future is currently unresolvable uncertainty about what will
then be the appropriate rate of return on capital to use for discounting. This paper shows that
there is a well-defined sense in which the ‘‘lowest possible’’ interest rate should be used for
discounting the far-distant future part of any investment project. Some implications are
discussed for evaluating long-term environmental projects or activities, like measures to
mitigate the possible effects of global climate change
With uncertainty about that extinction rate this Weitzman paper’s argument is relevant: