Investor Presentaiton
The St. Petersburg Paradox
Bernoulli considered the following game:
▷ The casino repeatedly flips a "fair" coin until it lands on heads.
▷ The casino then pays the player $2, where n is the number of times
the coin was flipped.
▷ What is a fair price for this game? i.e. How much money should a
player be willing to pay to play it?
The paradox is that the expected winnings are infinite-the average
amount won has no upper limit—but no reasonable person would
pay even $100 to play, let alone their entire wealth.
▷ Bernoulli (1738) worked on the paradox in his paper Exposition of a
new theory on the measurement of risk.
▷ His solution introduced the idea of utility: A gambler does not bet
based on expected winnings but rather expected utility. As wealth
increases, more money does not yield as much utility.
Expected utility-and equivalent formulations expected loss and
expected regret-have become the standard framework for making
decisions under uncertainty.View entire presentation