(though there may always be arbitrage/insurance between people of different risk tolerances).
The efficient market price for increasing and decreasing risk is zero.
Easy example of increasing risk: I create two futures contracts, A which will pay out £50 if a coin comes out heads, and cost you £50 if that coin comes out tail. The second contract is B, where the outcomes is reversed. A and B together is exactly the same as nothing at all; if sold seperately, I've just created risk from nothing.
In practice there will be insurance opportunities; but the profits may be tiny.
I'd be interested to hear your thoughts on whether or to what degree we may be able to discern the kernel of a human utility function.
I think, not at all. Our preferences are too transitive, dependent, and inconsistent. The real question is, whether we can construct a utility function that we'd find acceptable; that is much more likely.
The efficient market price for increasing and decreasing risk is zero.
If you can find people with complementary attitudes toward risk. Your example does indeed create risk--but in a risk-averse world, nobody would want to buy those contracts. Insurance arises from large entities with high capital and thus high relative risk-neutrality assuming the risk of smaller, more risk-averse entities for a price. If this market can be made efficient, the profits thus gained may be small, but insofar as all private insurance-providing organizations should be ris...
I prefer the movie Twelve Monkeys to Akira. I prefer Akira to David Attenborough's Life in the Undergrowth. And I prefer David Attenborough's Life in the Undergrowth to Twelve Monkeys.
I have intransitive preferences. But I don't suffer from this intransitivity. Up until the moment I'm confronted by an avatar of the money pump, juggling the three DVD boxes in front of me with a greedy gleam in his eye. He'll arbitrage me to death unless I snap out of my intransitive preferences and banish him by putting my options in order.
Arbitrage, in the broadest sense, means picking up free money - money that is free because of other people's preferences. Money pumps are a form of arbitrage, exploiting the lack of consistency, transitivity or independence in people's preferences. In most cases, arbitrage ultimately destroys itself: people either wise up to the exploitation and get rid of their vulnerabilities, or lose all their money, leaving only players who are not vulnerable to arbitrage. The crash and burn of the Long-Term Capital Management hedge fund was due in part to the diminishing returns of their arbitrage strategies.
Most humans to not react to the possibility of being arbitraged by changing their whole preference systems. Instead they cling to their old preferences as much as possible, while keeping a keen eye out to avoid being taken advantage of. They keep their inconsistent, intransitive, dependent systems but end up behaving consistently, transitively and independently in their most common transactions.
The weaknesses of this approach are manifest. Having one system of preferences but acting as if we had another is a great strain on our poor overloaded brains. To avoid the arbitrage, we need to scan present and future deals with great keenness and insight, always on the lookout for traps. Since transaction costs shield us from most of the negative consequences of imperfect decision theories, we have to be especially vigilant as transaction costs continue to drop, meaning that opportunities to be arbitraged will continue to rise in future. Finally, how we exit the trap of arbitrage depends on how we entered it: if my juggling Avatar had started me on Life in the Undergrowth, I'd have ended up with Twelve Monkeys, and refused the next trade. If he'd started me on Twelve Monkeys, I've had ended up with Akira. These may not have been the options I'd have settled on if I'd taken the time to sort out my preferences ahead of time.
For these reasons, it is much wiser to change our decision theory ahead of time to something that doesn't leave us vulnerable to arbitrage, rather than clinging nominally to our old preferences.
Inconsistency or intransitivity leaves us vulnerable to a strong money pump, so these we should avoid. Violating independence leaves us vulnerable to a weak money pump, which also means giving up free money, so this should be avoided too. Along with completeness (meaning you can actually decide between options) and the technical assumption of continuity, these make up the von Neumann-Morgenstern axioms of expected utility. Thus if we want to avoid being arbitraged, we should cleave to expected utility.
But the consequences of arbitrage do not stop there.
Quick, which would you prefer, ¥10 000 with certainty, or a 50% chance of getting ¥20 000? Well, it depends on how your utility scales with cash. If it scales concavely, then you are risk averse, while if it scales convexly, then... Stop. Minus the transaction costs, those two options are worth exactly the same thing. If they are freely tradable, then you can exchange them one for one on the world market. Hence if you price the 50% contract at any value other than ¥10 000, you can be arbitraged if you act on your preferences (neglecting transaction costs). People selling to or buying contracts from you will make instant free money on the trade. Money that would be yours instead if your preferences were other.
Of course, you could keep your non-linear utility, and just behave as if it were linear, because of the market price, while being risk-averse in secret... But just as before, this is cumbersome, complicated and unnecessary. Exactly as arbitrage makes you cleave to independence, it will make your utility linear in money - at least for small, freely tradable amounts.
In conclusion:
Addendum: If contracts such as L = {¥20 000 if a certain coin comes up heads/tails} were freely tradable, they would cost ¥10 000.
Proof: Let LH be the contract that gives out ¥20 000 if that coin comes out heads; LT be the contract if that same coin comes out tails. LH and LT together are exactly the same as a guaranteed ¥20 000. However, individually, LH and LT are the same contract - 50% chance of ¥20 000 - thus by the Law of One Price, they must have the same price (you can get the same result by symmetry). Two contracts with the same price, totalling ¥20 000 together: they must individualy be worth ¥10 000.