St. Petersburg Paradox Entry Fee - Quant Trader Interview Question
Difficulty: Medium
Category: Betting Games
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, expected-value, utility-theory, paradox
Problem Description
You are offered to play the St. Petersburg game. A fair coin is flipped repeatedly until the first time it lands on heads. The payoff is $2^n$, where $n$ is the number of flips it takes to get the first head.
What is the maximum amount you would rationally pay to play this game once, assuming your utility function is $U(x) = \sqrt{x}$, where $x$ is the payoff?
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