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I do not think one trillion dollars would buy enough anti matter to zap an asteroid considering the rate at which it is produced at present.
How big does an asteroid need to be so that when you blow it up, its own gravity pulls it back together?
I suppose one should find it disturbing that in lay-terms, impact events are often described in "Hiroshima Bomb", or ...sorry, you cannot view external links. To see them, please
REGISTER or LOGIN suggests asteroid impact extinction events every 26 million years, with the next one due in about 15 million years. Whether or not Nemesis exists... there may be some periodicity to the "Big Ones".However, I think the idea of seed banks in naturally cold areas is good. Perhaps we should also build an seed&egg&tissue bank in Antarctica. Or, on the moon. Access would be a pain, but one could put a seed&egg&tissue bank in a polar crater on the moon. Temperature could be held very low. It would be reasonably protected, except for cosmic rays, which could be protected from with a good vault design. If the Earth got pummeled by a meteor shower, the moon might also get hit, although having both a North and a South polar vault would give some amount of protection.A permanent off-planet colony (moon, Mars, Venus, or elsewhere) would, of course, also give an amount of redundant protection.