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Difficulty: Hard
Category: Conditional Expected Value
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: auction, winner's-curse, bidding, expected-value, probability, uniform-distribution
You are participating in a sealed-bid auction for an antique clock. The true value (V) of the clock to the market is uniformly distributed between (0) and (100) (i.e., $$( V \sim \mathcal{U}0,100)$$. However, due to your unique expertise, the clock is worth 1.5 times its market value to you. That is, your valuation is (1.5V). You must submit a single bid (B). If your bid is the highest (or only) bid, you win the auction and pay your bid amount (B). If your bid is not the highest, you do not win
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