Adverse selection when the prior is not 50/50
Asked at Optiver, Jane Street
An asset is worth or , but now the market believes the high state is more likely: , . A fraction of traders are informed (know , trade the profitable side); the rest are noise. Competition forces zero expected profit on each side.
What are the break-even bid and ask now, and is the mid-quote still the unconditional mean?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.