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Mar 1, 2012 at 0:10 comment added Anthony Quas The specific form of the question (where the cone is exactly the positive orthant) shows up in option-pricing models. In Ross's textbook, An Elementary Introduction to Mathematical Finance, the exact question is called the Arbitrage Theorem.
Feb 29, 2012 at 22:34 history answered Igor Rivin CC BY-SA 3.0