Puzzle for August 2006.
Prediction markets trade in contracts that pay off according to whether some future event occurs. If the event occurs the contract pays off 1 unit otherwise the contract becomes worthless. The price of a contract can be interpreted as the market's opinion on the probability that the future event will occur.
Suppose individuals A and B think the probability that the future event will occur is p or q respectively. Suppose A and B have risk capital X and Y respectively. Suppose A and B invest so as to maximize the expected log of their capital. What price r for the contract will clear the market (ie assure that the sum of the demand for the contract from A and B is 0). We are assuming contracts can be sold short which corresponds to risking (1-r) units to gain r units if the event does not occur. We are also ignoring all frictional costs like commissions or interest.
I came up with this problem myself but I doubt it is original. Please don't submit solutions you haven't derived yourself.
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08/02/2006 @ 03:30 PM EST
Solution: 09/01/2006 @ 10:00 AM EST
List Updated: 09/07/2006 @ 10:00 AM EST
People who answered correctly:
Ross Millikan (08.02.2006 @04:18:54 PM EDT)
Joe Fendel (08.02.2006 @06:10:04 PM EDT)
V. Balakrishnan (08.02.2006 @10:44:56 PM EDT)
Vincent Vermaut (08.03.2006 @02:44:04 AM EDT)
Alan Murray (08.03.2006 @10:21:02 AM EDT)
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James Dow Allen (08.04.2006 @09:28:38 AM EDT)
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Rob Berger (08.04.2006 @04:51:38 PM EDT)
Ashish Mishra (08.04.2006 @09:32:10 PM EDT)
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