While being widely seen as an example of exactly why bigger, better government is needed to ameliorate or somehow prevent mega-natural resource and pollution crises, anarcho-theorist and Seasteading guru Patri Friedman takes a swing at explaining how and why a truly free market, including some changes in current corporate liability law, has a better chance of managing such disasters. The key:
BP is worth about $250B, and current estimate are the spill will cost them $1B. So damages after the fact can actually work. I think the $1B number is very low, but even if it is off by two orders of magnitude, they could afford to pay $100B in damages.
Unfortunately, there are laws which limit the liability of oil companies for disasters, and thus prevent them from having the proper incentive. (Krugman blames libertarians for these laws, which is ridiculous, libertarianism != crony capitalism, and there is nothing libertarian about limiting damage liability). So BP can't legally be charged the full cost of the cleanup—which is a government failure, not a market failure. Government implemented a policy which benefits special interests—big surprise.
Now, this idea of damages after the fact doesn't hold for all disasters—it just happens that the oil industry has the largest companies in the world, so they can pay damages even for very large disasters. In other industries, where potential damages exceed company assets, I think the answer is to require liability insurance with amounts large enough to cover worst-case damages. Then you get a free-market price put on the risks (by the insurance market), which gives companies the right incentive to avoid risky behavior even if the damages are to large for them to pay.
If you have a 1% chance of causing $1B in damages with your $100M company, insurance will charge you $10M/year (plus a little profit for them). Thus the company must bear the expected value of the disaster—which is exactly the optimal thing, it's the true cost of the activity. Thus they will only take this risk if the benefit is greater than the cost. Whereas if they don't have to have insurance, they face only a $1M/year cost (1% of the $100M max they will have to pay since that's all they have), which is not the true cost of their activities. Note that one way to bring about this situation is to remove the limited liability of corporations for damages, which I favor on moral and practical grounds. (Limited liability for business debts, or any other contractual interactions with persons, can simply be done through a consensual contract. But why should liability be limited when you hurt people you didn't get consent from?). If shareholders, officers, and staff were personally liable for damages in excess of the corporation's assets, you can bet your ass that every venture would have insurance!
You could argue with Friedman about this, if you care to, on Reason's first cruise ship excursion, early next year.