Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Prove the following result in the derivation of the asymptotic optimality of the bid-price control policy. Let X be a random variable with finite first and second order moments, i.e., E[X] = µ < +∞, E[(X − E[X])^2] = σ^2 < +∞. Let x+ = max{x, 0}. Prove the following: ∀m ∈ R,
E[(X − m)+] ≤ (√ (σ2 + (m − µ)^2) − (m − µ))/2.
Hint: You can without loss of generality let m = 0
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