24th July 2006, 06:37 PM
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Member
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Join Date: Jan 1970
Location: Sydney
Posts: 402
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Quote:
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Originally Posted by crash
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Peter's gamble
Peter asks me for a bid on the following gamble. I get to
flip a coin up to 10
times. If I get heads on the kth
flip, 1 . k . 10, I collect 2k1 and stop. If I
manage to
flip tails 10 times in a row, I collect 1024.
How much should I offer Peter for this gamble? In theory, the value of
this gamble is
· 210
(1=2 · 1 + 1=4 · 2 + 1=8 · 4 + :::+ 1=210 · 29) + 1=210
= 10 · 1=2 + 1
=6.
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The Peter's Gamble example should make sense if you try to work through it with a spreadsheet.
The amazing thing to me, is that it illustrates Huygens propensity for inventing incredibly useful things.
After he invented Expectation he then had to prove it. So to do that he invented Hedging! I'd always thought that Hedging was a modern concept.
The example illustrates Hedging as a proof of Expectation.
It shows how you can convert an Expectation of 6, with huge volatility into a guaranteed return of 6. By using appropriate hedge bets.
Right now there appear to be around 10 documented investor/gamblers each heading towards a billion from scratch. In no small part thanks to Huygens.
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