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Also, this is more of a gambling thing, but it was quite popular a few years back. Have you heard of a death/dead pool? They usually follow the calendar year, and the participant chooses a set number of people s/he thinks will die in the next year. This is a pretty famous one...

Robert Shiller would... By some strange machinations of chance, I met Shiller a few days ago and figured I might as well ask him about the contents of this post. First, I have to say that he was absolutely gracious and quite generous with his time. He was humble and engaging and I walked away...

What a fun problem!! We can start with a trig identity: \( sin^2(x) + cos^2(x) = 1^2 \) Extending that, \( \sum_{k=0}^{90} sin^2(k) + \sum_{j=0}^{90} cos^2(j) = \sum_{i=0}^{90} 1^2 \) By symmetry, \( \sum_{k=0}^{90} sin^2(k) + \sum_{j=0}^{90} sin^2(j) = \sum_{i=0}^{90} 1 \) The...

another approach I don't know of any OTC derivatives. Are you generally curious about their existence or are you trying to offset risk? If it's the latter, you could try cross-hedging. If you can find a derivative for an asset that correlates highly with the GDP, you can mitigate your exposure...

I'll give a go... P is one-to-one. So P(N) is a product of the factors, and each of the factors has a unique prime factorization. We can decompose P(N) into a product of these prime factorizations, but then we won't be able to permute it into different factors, so P(N)=P(M) => N = M. I would...