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Announcements, Events, and Seminars
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Colloquium
Statistics
Cosponsor: Center for Computational Finance and Economic Systems
The St. Petersburg Paradox and the Crash of High-Tech Stocks in 2000
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Donald Richards
Professor Statistics
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Penn State |
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Monday, February 6, 2006
Time: 4:10 PM
to 5:00 PM
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1070 Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA
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| abstract |
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Peter repeatedly tosses a fair coin until it comes up heads. Peter agrees to pay Paul $2 if a head appears on the first toss, $4 if he gets the first head on the second toss, $8 if he gets the first head on the third toss, and so on. How much should Peter charge Paul as an entrance fee to this game so that the game is fair to both players? This game, the classic example of a St. Petersburg game, was first described in 1713 by Nicolaus Bernoulli in a letter to Remond de Montmort. It is paradoxical that no finite entrance fee can make the game fair to both players. We will discuss the history of St. Petersburg games and some recent examples of modified St. Petersburg games, such as the game show "Who Wants to be a Millionaire?", and Cleveland Indians major league baseball player Ken Harrelson (who offered to play the entire 1969 baseball season without salary except for 50 cents doubled for every home run he hit; so his salary would be 50 cents if he hit only 1 home run, $1 if he hit 2 home runs, $2 if he hit 3 home runs, and so on). Finally, we will see how the St. Petersburg paradox easily predicted the crash of U.S. high-tech stocks in 2000. |
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