Effect of prediction of later catastrophe Say a catastrophic worldwide event is predicted likely for exactly 100 years from now, but it will not affect anyone til then. Say a large meteor hit.

Would markets budge much?

My only relevant observation is governments tend to invest in the future, but begrudgingly. (Climate change). So there will be some money in disaster aversion etc.
This is a very open ended question, that could be researched. I can start to give some direction. For a realistic answer, one of the most important assumptions to your questions is how strongly everyone believes a meteor will hit 100 years from now, and second, how strongly everyone believes it is preventable/management. 

Consider Two Scenarios:

A. The meteor will hit in 100 years. In the first 2 years, we developed a solution to it all, and everyone is convinced it will work. Will markets budge much? Probably not much afterward. Depending on the cost of the solution (\$1 million vs. \$10 trillion) markets may have moved.

B. The meteor will hit in 100 years. Everyone has fully accepted there is nothing we can do about it, and we all will be annihilated. Market will budge significantly, especially as the date gets closer. People's investment for future will change, how we think about raising kids, etc. How markets will change would be pretty hard to describe, but there may be outside literature that postulates ideas.

Overall, the biggest factor is humanities belief in their future. You can start by modeling the distribution of humanity that believes we will exist for $t$ more years. This now gets into probability theory.