Great question. The setup here assumes zero interest rates—in particular, I’m implicitly allowing borrowing without interest via short sales (real-world short sales charge interest). Once we allow for nonzero interest, there’s a rate charged to borrow, and the price of each asset is its discounted expected value rather than just expected value. That’s one of several modifications needed in order to use this theorem in real-world finance. (The same applies to the usual presentation of the Dutch Book arguments, and the same modification is possible.)
Great question. The setup here assumes zero interest rates—in particular, I’m implicitly allowing borrowing without interest via short sales (real-world short sales charge interest). Once we allow for nonzero interest, there’s a rate charged to borrow, and the price of each asset is its discounted expected value rather than just expected value. That’s one of several modifications needed in order to use this theorem in real-world finance. (The same applies to the usual presentation of the Dutch Book arguments, and the same modification is possible.)