Ways to invest your wealth if you believe in a high-variance future?

To give an example answer to my own question, the classic asset class of real estate, a.k.a. buy a house, is actually a pretty good idea under many of these scenarios. If money loses value, you still have shelter and a place to keep your stuff safe!

I think the different categories of possible future imply different strategies, which in turn has implications for what you should do.

In the case of a singularity type event, the most important element is that you live to see it. By definition it's hard or impossible to predict what the world will be like afterwards, which reduces the value of e.g. having lots of wealth going into a singularity. However it increases the expected value of living until then. Similar arguments apply to a post-scarcity world.

In the case of a disaster, the value some holdings may decline even to zero (e.g. if there are no more stock markets, equity holdings are pretty useless). In that case, physical possessions that either hold wealth or are directly useful (e.g. shelter, food, guns, medical supplies) radically increase in value.

Note that those kinds of things may also help you live longer! Prepping for a medium or large disaster is like buying insurance. Probably you won't need it, and it's negative expected value in dollars, but can be plus expected value in utility. 

Finally, investments in your physical health help in all situations. You'll live longer to reach the glorious future if one awaits, and you'll be better off in many downside scenarios.

TL;DR: buy canned food, learn to fire a gun, and hire a personal trainer.

Cryonics becomes a better investment because your getting revived is highly correlated with how good the future is.  The run up to a singularity will cause real interest rates to increase as investment opportunities grow.  An actual singularity might cause money to lose all its value.  

I think if you look up antifragile investment you find a lot of discussion of exactly this problem. As far as I understand, the idea is that most investments have limited downsides (at most, you lose what you put in) but may have limitless upsides in low-probability scenarios. Then you can make many small investments of this kind, so that when ones pays off, it's more than enough to pay you back from the loss of the rest. Taking your example of the nuclear bunker, if you could build one with 1% of your wealth or less, in this frame of mind probably you should. Or less dramatically, invest a bit into any technology that could reach world-changing level even if it looks unlikely, plus buy a house as well as a cabin far away from any city. Learn a little bit of skills that could be useless or incredibly useful, depending on the future.

The answers you are suggesting are more related to safe/robust investment (I'm uncertain on the correct term), i.e. investment which should be useful whatever happens, but has a capped upside. Both maintain good health and buy a house count in this category. I'm not more qualified to give specific advice here than anyone else, but if you ask yourself "what would a standard prudent person do" you're basically there.

Robust investment is what most people do in practice, and it's probably a good thing because I think antifragile investment is too easy to screw up. But under some assumption on the nature of the high variance, which I think match the kind of future scenarios that you listed, well-thought antifragile strategies could be much better. At the very least, you can copy the idea of not putting all eggs in one basket, even if you don't go all the way to make many small gambles in the expectation that at least one will pay off.

The main change I've made (which depends some on thinking that you can see at least some of the variance coming) is to keep more of my wealth as dollars in a brokerage account where I can buy options. [This does assume that, say, you would have known to sell puts in the first half of Feb 2020.]

I don't know why you'd be worried about having wasted your money on a nuclear bunker if the singularity or a post-scarcity world arrives, but here are my answers.

Do the important things for your health. DNA and allergy assessments should be less than 1k USD total, but they're very useful for all your scenarios.

After that, your second best investment will be in your social connections. Any way you can spend money to facilitate the gain of quantity and quality of your friends and family is very likely to pay off in your scenarios. This might include raising your social status through conspicuous consumption, paying off the medical debts of a friend, or sending your kid to college. There's nothing quite as powerful as having an advocate. Might seem like a cop-out answer, but it is effective.

Buy the maximum recommended disaster rations, and then put the rest of your money into a tech stock ETF.