L2

St. Petersburg Paradox

Senior Quant · Brainteasers & Logic

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Game pays $2ⁿ when the first head appears on flip n. How much would you pay to play?

Question

A game pays 2n2^n if the first head appears on flip nn. Compute the expected winnings. Would a rational agent pay $1,000 to play? Resolve the St. Petersburg paradox using logarithmic utility. What does this imply about risk-neutral pricing of unbounded payoffs?